It was Peter who said that "baptism now saves you" in 1 Peter 3:21.
Here is the verse in the New American Standard Version and the Revised Standard Version:
"And corresponding to that, baptism now saves you--not the removal of dirt from the flesh, but an appeal to God for a good conscience--through the resurrection of Jesus Christ" (NASB).
"Baptism, which corresponds to this, now saves you, not as a removal of dirt from the body but as an appeal to God for a clear conscience, through the resurrection of Jesus Christ" (RSV).
"Appeal" has been defined as "a call for aid, support, mercy, etc.; an earnest request or entreaty; to appeal is to ask earnestly for help or support....", which helps us to understand how that through the act of baptism, people are "calling" on the name of the Lord (see Acts 22:16).
And also consider Acts 2:21, 36-38. In this first verse, Peter quoted Joel's prophecy that "...everyone who calls on the name of the Lord shall be saved"; but according to the account, the way this was done was not by merely praying a "sinner's prayer." Rather, it was accomplished by their faith in Jesus (v. 36), along with their repentance and water baptism (v. 38). They sought God's mercy and forgiveness by meeting His conditions.
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The King James Version states in 1 Peter 3:21 that "...baptism doth also now save us..." and does so as "the answer of a good conscience toward God...."
It's interesting to note that the Greek word rendered as "answer" in this verse is defined as "a question, an asking; enquiry after, seeking by enquiry" (A Critical Lexicon and Concordance to the English and Greek New Testament by E. W. Bullinger).
So, clearly, baptism is not for those "already saved"; but rather for penitent believers who want to appeal to God for salvation. (Baptism is part of the condition one must meet to benefit from the death of Christ.