12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
First it says we are buried with him, and risen with him,
in baptism. Then, the very next verse says we are 'quickened together with him'. This being made alive together with him corresponds to being 'risen with him'. Since being risen with him occurs in baptism, we are made alive together with him in baptism. Therefore, baptism is part of regeneration.
Furthermore,
Acts 22:16 says 'be baptised and wash away your sins, calling on the name of the Lord'. Thus, according to the NT, washing away of sins is united to baptism in the name of the Lord.