Unfortunately this is not quite what Paul wrote. The NSRV has added the word 'as' on two occasions.
Here is the NKJV translation: 'there is also an antitype that saves us - baptism (not the removal of the filth of the flesh, but the answer of a good conscience towards God), through the resurrection of Jesus Christ, who has gone into heaven and is at the right hand of God, angels and authorities and powers having been made subject to Him.'
The point is that the subordinate clauses tell us what the baptism that saves is not, and what it actually is. It is not getting wet - the removal of dirt or filth from the flesh. The getting wet is an ordinance of Jesus Christ (Matt. 28:19) and not be be ignored or disobeyed, but it does not save. The baptism that saves is 'the answer [or 'pledge'] of a good conscience towards God.' It can only be the baptism of the Holy Spirit which enables the one saved by grace to obey the ordinance of Christ. That seems to have been your experience; it was also mine.
I rather think they did.
Christians, with the exception of those whose
theology is Baptist (with or without add-ons), believe that the grace of God for salvation is normatively conferred upon the believer through water baptism. And this was the virtually the unanimous view of the Church for 1600 years—even surviving the first 100 years of the Protestant Reformation!
However, this was NOT my experience! I was saved and filled with the Holy Spirit for several weeks
before I was baptized in water by immersion. Millions of other Christians have had a similar experience. But Peter did not share that experience, and in his first epistle, he wrote,
1 Peter 3:21 ὃ καὶ ὑμᾶς ἀντίτυπον νῦν σῴζει βάπτισμα, οὐ σαρκὸς ἀπόθεσις ῥύπου ἀλλὰ συνειδήσεως ἀγαθῆς ἐπερώτημα εἰς θεόν, δι’ ἀναστάσεως Ἰησοῦ Χριστοῦ
22 ὅς ἐστιν ἐν δεξιᾷ τοῦ θεοῦ πορευθεὶς εἰς οὐρανὸν ὑποταγέντων αὐτῷ ἀγγέλων καὶ ἐξουσιῶν καὶ δυνάμεων. (NA28)
21. And baptism, which this prefigured, now saves you—not as a removal of dirt from the body, but as an appeal to God for a good conscience, through the resurrection of Jesus Christ,
22. who has gone into heaven and is at the right hand of God, with angels, authorities, and powers made subject to him. (NRSV)
In each of these two verses, there is only one verb in the indicative mood—and hence there is only one main clause in each of the verses. In verse 21, the verb that is in the indicative mood is the verb σῴζει (saves) giving us the primary clause, “baptism now saves you.” All of the other clauses are subordinate clauses, and being subordinate clauses, they can add qualifiers, but they cannot change the primary clause, “baptism now saves you.” Peter wrote it, but I did not experience it. A whole lot has happened in the church since Peter penned these words, and they are not applicable to everyone today.
However, there are some people today who insist that Peter is NOT teaching here about water baptism, but spiritual baptism even though Peter himself wrote,
1 Peter 3:20. who in former times did not obey, when God waited patiently in the days of Noah, during the building of the ark, in which a few, that is, eight persons, were
saved through water.
21. And baptism, which this prefigured, now saves you--not as a removal of dirt from the body, but as an appeal to God for {Or [a pledge to God from]} a good conscience, through the resurrection of Jesus Christ,
22. who has gone into heaven and is at the right hand of God, with angels, authorities, and powers made subject to him.
Indeed, even Calvin expressly taught that in this passage of Scripture Peter is teaching about water baptism.