John 3 is a well-known text that supports the doctrine of baptismal regeneration. For an exegesis, see my article:
Some believe that Jesus is basing his comments, in part, on various Old Testament texts, such as various passages from Ezekiel, that speak of God pouring water on people and cleaning them inwardly (i.e., regenerating them), such as Ezek 16:9; 37:9-10. Interestingly, this also informed a lot of the debate about the nature of water baptism during the Reformation.
Henry VIII, while still a faithful Catholic, wrote a response to Luther’s 1520 On the Babylonian Captivity of the Church entitled Assertio Septem Sacramentorum (“Defence of the Seven Sacraments”) in 1521. On the discussion of baptism, Henry VIII wrote:
But because all agree in this, That Sacraments are efficacious Signs of Grace, Luther rejects the one as well as the other: For my Part, as I do not know which of the Opinions are the truest, so neither dare I be so bold as to condemn either of them. For that very Opinion which now is the less assented to, to wit, ‘That the Water by Virtue of the Word, has an occult Power of purging the Soul;’ seems not to be altogether absurd. For if we believe, that Fire has any Influence over the Soul, either to punish or purge Sins; what hinders that Water should, by the Power of God (by whom also the other Thing is done) penetrate to wash away the Uncleanness of the Soul? Which Opinion seems to be much confirmed by the Words of St. Augustine, when he says, ‘The Water of Baptism toucheth the Body, and Washes the Heart;’ and also that of St. Beda, who says ‘That Christ, by the Touch of his most pure Flesh, has given the Water a regenerate Power.’ Likewise that of the Prophet Ezekiel seems to incline towards this, ‘I washed thee with Water, and cleansed by thy Blood from thee’ (Ezech. xvi. 9); Which Words, though they were spoken in Times past, before Baptism was instituted, are, notwithstanding, (according to the Custom of the Prophets) understood of the future. Neither speaks he only of the washing of the Body, in which nothing is worthy the Praedication of a Prophet; nor was ever any other Washing which washed the Crimes of the Soul, but the Sacrament of Baptism, of which Ezekiel seems to have spoken in the Person of God; prophesying, that there should be a future Cleansing in the Sacrament of Baptism, by the washing Font of Water: Which, by the same Prophet is more plain a littler after, when he speaks of the future; ‘I will pour out, saith he, clear Water upon you, and I will cleanse you from all your Iniquities’ (Ezech. xxxvi.25). Whether does he not here promise a Cleansing by Water? Yet Zecharias seems to unfold the Matter more apparently, when he says, ‘Living Water shall flow out from Jerusalem, the one Half to the Eastern Sea, and the other Half to the great sea’ (Zach. xiv 8). Does not this Discourse manifest not us the Figure of Baptism, viz. Water flowing from the Church, which should purge both original and actual Sin? which he does not call dead, but living; that he might demonstrate, as I suppose, That, by the secret Sanctification of God, the Force of spiritual Life is infused into a corporeal Element. Although I do not presumes to judge, (as I have said already,) nor am I curious, after what Manner God infuses Grace by the Sacraments, because his Ways are inscrutable: Yet I believe, that by one way or other, this Water should not be idle, where he fore-tells so many, and so great Things, were to be done by Water; especially, since Water, Salt, and other corporeal Things, do receive spiritual Force, by the Word of God, without the Sacrament of Faith; unless all those Things should be spoken in vain; in which Lights, Fire, Water, Salt, bread, the Altar, Vestments, and Rings, are either adjurged by Exorcisms, or blessed by the Invocation of Grace. (Henry VIII, Assertio Septem Sacramentorum or Defence of the Seven Sacraments, ed. Louis O’Donovan [New York: Benziger Brothers, 1908], 306, 308, italics in original)
What is rather interesting is that Henry appealed to the various Ezekiel texts to support his doctrine of baptism as well as infused righteousness.