I have addressed Acts 2:38 before, showing that, when exegeted properly, it clearly teaches baptismal regeneration:
In this post, I wish to add to the body of evidence by presenting quotations from early Christian writers who used Acts 2:38 in a manner similar to Latter-day Saints and others who accept the biblical teaching of baptismal regeneration.
For whereas in the Gospels, and in the epistles of the apostles, the name of Christ is alleged for the remission of sins; it is not in such a way as that the Son alone, without the Father, or against the Father, can be of advantage to anybody; but that it might be shown to the Jews, who boasted as to their having the Father, that the Father would profit them nothing, unless they believed on the Son whom He had sent. For they who know God the Father the Creator, ought also to know Christ the Son, lest they should flatter and applaud themselves about the Father alone, without the acknowledgment of His Son, who also said, “No man cometh to the Father but by me.” But He, the same, sets forth, that it is the knowledge of the two which saves, when He says, “And this is life eternal, that they might know Thee, the only true God, and Jesus Christ, whom thou hast sent.” Since, therefore, from the preaching and testimony of Christ Himself, the Father who sent must be first known, then afterwards Christ, who was sent, and there cannot be a hope of salvation except by knowing the two together; how, when God the Father is not known, nay, is even blasphemed, can they who among the heretics are said to be baptized in the name of Christ, be judged to have obtained the remission of sins? For the case of the Jews under the apostles was one, but the condition of the Gentiles is another. The former, because they had already gained the most ancient baptism of the law and Moses, were to be baptized also in the name of Jesus Christ, in conformity with what Peter tells them in the Acts of the Apostles, saying, “Repent, and be baptized every one of you in the name of the Lord Jesus Christ, for the remission of sins, and ye shall receive the gift of the Holy Ghost. For this promise is unto you, and to your children, and to all that are afar off, even as many as the Lord our God shall call.” Peter makes mention of Jesus Christ, not as though the Father should be omitted, but that the Son also might be joined to the Father. (Cyprian, Epistle LXXII, 17)
In order, therefore, that we return not to our former vomit, let us henceforward discipline ourselves. For that we must repent beforehand, and desist from our former evil, and so come forward for grace, hear what John says, and what the leader of the apostles says to those who are about to be baptized. For the one says, "Bring forth fruit worthy of repentance, and begin not to say within yourselves, we have Abraham to our Father;" and the other says again to those who question him, "Repent ye and be baptized every one of you in the name of the Lord Jesus Christ." Now he who repents, no longer touches the same matters of which he repented. On this account, also, we are bidden to say, "I renounce thee, Satan," in order that we may never more return to him. As therefore happens in the case of painters from life, so let it happen in your case. For they, arranging their boards, and tracing white lines upon them, and sketching the royal likeness in outline, before they apply the actual colors, rub out some lines, and change some for others, rectifying mistakes, and altering what is amiss with all freedom. But when they put on the coloring for good, it is no longer in their power to rub out again, and to change one thing for another, since they injure the beauty of the portrait, and the result becomes an eyesore. Consider that thy soul is the portrait; before therefore the true coloring of the spirit comes, wipe out habits which have wrongly been implanted in thee, whether swearing, or falsehood, or insolence, or base talking, or jesting, or whatever else thou hast a habit of doing of things unlawful. Away with the habit, in order that thou mayest not return to it, after baptism. The laver causes the sins to disappear. Correct thy habits, so that when the colors are applied, and the royal likeness is brought out, thou mayest no more wipe them out in the future; and add damage and scars to the beauty which has been given thee by God. Restrain therefore anger, extinguish passion. Be not thou vexed, be sympathizing, be not exasperated, nor say, "I have been injured in regard to my soul." No one is injured in regard to the soul if we do not injure ourselves in regard to the soul; and how this is, I now say. Has any one taken away thy substance? He has not injured thee in regard to thy soul, but thy money. But if thou cherish ill-will against him, thou hast injured thyself in regard to thy soul. For the money taken away has wrought thee no damage, nay has even been profitable, but thou by not dismissing thine anger wilt give account in the other world for this cherishing of ill-will. Has any one reviled thee and insulted thee. He has in no way injured thy soul, and not even thy body. Hast thou reviled in return and insulted? Thou hast injured thyself in regard to thy soul, for for the words which thou hast said thou art about to render account there; and this I wish you to know chiefly of all, that the Christian, and faithful man, no one is able to injure in regard to the soul, not even the devil himself; and not only is this wonderful, that God hath made us inaccessible to all his designs, but that he has constituted us fit for the practice of virtue, and there is no hinderance, if we will, even though we be poor, weak in body, outcast, nameless, bondservants. For neither poverty, nor infirmity, nor deformity of body, nor servitude, nor any other of such things could ever become a hinderance to virtue; and why do I say, poor, and a bondservant, and nameless? Even if thou art a prisoner, not even this would be ever any hinderance to thee as regards virtue. And how this is I proceed to say. Has any of thy household grieved thee and provoked thee? dismiss thy wrath against him. Have bonds, and poverty, and obscurity been any hinderance to thee in this respect? and why do I say hinderance? They have both helped and contributed to restrain pride. Hast thou seen another prospering? do not envy him. For not even in this case is poverty a bar. Again, whenever thou needest to pray, do so with a sober and watchful mind, and nothing shall be a bar even in that case. Show all meekness, forbearance, self-restraint, gravity. For these things need no external helps. And this especially is the chief point about virtue, that it has no necessity for wealth, power, glory, nor anything of that kind, but of a sanctified soul alone, and it seeks for nothing more. And behold, also, the same thing happening in respect of grace. For if any one be lame, if he has had his eyes put out, if he be maimed in body, if he has fallen into the last extremity of weakness, grace is not hindered from coming by any of these things. For it only seeks a soul receiving it with readiness, and all these external things it passes over. For in the case of worldly soldiers, those who are about to enlist them for the army seek for stature of body and healthy condition, and it is not only necessary that he who is about to become a soldier should have these alone, but he must also be free. For if anybody be a slave, he is rejected. But the King of Heaven seeks for nothing of this kind, but receives slaves into his army, and aged people, and the languid in limb, and is not ashamed. What is more merciful than this? What could be more kind? For he seeks for what is in our own power, but they seek for what is not in our power. For to be a slave or free is not our doing. To be tall, again, or short is not in our own power, or to be aged, or well grown, and such like. But to be forbearing and kind, and so forth, are matters of our own choice; and God demands of us only those things of which we have control. And quite reasonably. For He does not call us to grace because of his own need, but because of doing us kindness; but kings, because of services required by them; and they carry men off to an outward and material warfare, but He to a spiritual combat; and it is not only in the case of heathen wars, but in the case of the games also that one may see the same analogy. For they who are about to be brought into the theatre, do not descend to the contest until the herald himself takes them beneath the gaze of all, and leads them round, shouting out and saying, "Has any one a charge against this person?" although in that case the struggle is not concerned with the soul, but with the body. Wherefore then dost thou demand proofs of nobleness? But in this case there is nothing of the kind, but all is different, our contest not consisting of hand locked in hand, but in philosophy of soul, and excellence of mind. The president of our conflicts does the opposite. For he does not take us, and lead us round and say, "Has any one a charge against this man?" but cries out, "Though all men, though demons, stand up with the devil and accuse him of extreme and unspeakable crimes, I reject him not, nor abhor him, but removing him from his accusers, and freeing him from his wickedness, thus I bring him to the contest. And this is very reasonable. For there indeed the president contributes nothing towards the victory, in the case of the combatants, but stands still in the midst. But here, the President of the contests for holiness becomes a fellow-combatant, and helper, sharing with them the conflict against the devil. (John Chrysostom, Instructions to Catechumens: Second Instruction, 3)
Of this name the Lord of all says, “The Lord God shall call His servants by another name which shall be blessed on the earth” and the following is the reason why the Church specially clings to this name. When the only-begotten Son of God was made man, then He was named Christ, then human nature received the beams of intellectual light; then the heralds of the truth shed their beams upon the world. Teachers of the Church, however, constantly used the names of the only begotten without distinction; at one time they glorify the Father the Son and the Holy Ghost; at another the Father with Christ and the Holy Ghost; yet as far as the sense is concerned there is here no difference. Wherefore after the Lord had commanded to baptize in the name of the Father and of the Son and of the Holy Ghost the blessed Peter said to them who received his preaching and asked what they must do, “Believe and be baptized every one of you in the name of our Lord Jesus Christ,” as though this name contained in itself all the potency of the divine command. The same teaching is clearly given us by the great Basil, luminary of the Cappadocians, or rather of the world. His words are “the name of Christ is the confession of the whole.” It indicates at once the Father, who anointed, the Son, who was anointed, and the Holy Ghost whereby He was anointed. Furthermore the thrice blessed Fathers assembled in council at Nicæa, after saying that we must believe in one God, the Father, added “and in one Lord Jesus Christ, the only begotten Son of God.” Thereby they teach that the Lord Jesus Christ is Himself the only begotten Son of God. (Letters of the Blessed Theodoret, Bishop of Cyrus: To an unknown correspondent)
And since this is so, remission of sins, seeing it is not given but by the Holy Spirit, can only be given in that Church which hath the Holy Spirit. For this is the effect of the remission of sins, that the prince of sin, the spirit who is divided against himself, should no more reign in us, and that being delivered from the power of the unclean spirit, we should thenceforward be made the temple of the Holy Spirit, and receive Him, by whom we are cleansed through receiving pardon, to dwell in us, to work, increase, and perfect righteousness. For at His first coming, when they who had received Him spake with the tongues of all nations, and the Apostle Peter addressed those who were present in amazement, they were pricked in heart, and said to Peter and to the rest of the Apostles, "Men and brethren, what shall we do?" show us. "And Peter said to them, Repent, and be baptized every one of you in the Name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost." In the Church truly in which was the Holy Ghost, were both brought to pass, that is, both the remission of sins, and the receiving of this gift. And therefore was it "In the Name of Jesus Christ;" because when He promised the same Holy Ghost; He said, "Whom the Father will send in My Name." For the Spirit dwelleth in no man without the Father and the Son; as neither doth the Son without the Father and the Holy Spirit, nor the Father without them. Their indwelling is inseparable, as their operation is inseparable; but sometimes they manifest them- selves separately by symbols borrowed from the creatures, not in their own substance; just as they are pronounced separately by the voice in syllables which occupy separately their own spaces, and yet they are not separated from each other by any intervals, or moments of time. For they never can be pronounced together, whereas they can never exist, except together. But as I have already said, and not once only, the remission of sins, whereby the kingdom of the spirit which is divided against himself is overthrown and driven out, and the fellowship of the unity of the Church of God, out of which this remission of sins is not, are regarded as the peculiar work of the Holy Spirit, with the cooperation doubtless of the Father and the Son, because the Holy Spirit is Himself in some sort the fellowship of the Father and the Son. For the Father is not possessed2 as Father by the Son and the Holy Spirit in common; because He is not the Father of Both. And the Son is not possessed as Son by the Father and the Holy Spirit in common; because He is not the Son of Both. But the Holy Spirit is possessed as the Spirit by the Father and the Son in common, because He is the One Spirit of Both. (Augustine, Sermon XXI, 33)