Peter's baptism is not to be confused with Paul's. Peter (as was Jesus) is still a part of the Israel kingdom age which did not end until 70AD so any effort to make Peter's soteriology line up with Paul's is doomed from the start. Peter, unlike Paul does not blush when he says "baptism now saves us". Peter's gospel of repentance for Israel includes water baptism:
Act 2:38 Then Peter said unto 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.
Water baptism was essential for the Jews because Israel had been contaminated (not cleansed) by the death of Christ:
Act 2:22 Ye men of Israel, hear these words; Jesus of Nazareth, a man
approved of God among you by miracles and wonders and signs, which God
did by him in the midst of you, as ye yourselves also know: Act 2:23
Him, being delivered by the determinate counsel and foreknowledge of
God, ye have taken, and by wicked hands have crucified and slain:
Act 2:24 Whom God hath raised up, having loosed the pains of death:
because it was not possible that he should be holden of it.
Num 19:11 He that toucheth the dead body of any man shall be unclean
seven days. Num 19:12 He shall purify himself with it on the third
day, and on the seventh day he shall be clean: but if he purify not
himself the third day, then the seventh day he shall not be clean.
Num 19:13 Whosoever toucheth the dead body of any man that is dead,
and purifieth not himself, defileth the tabernacle of the LORD; and
that soul shall be cut off from Israel: because the water of
separation was not sprinkled upon him, he shall be unclean; his
uncleanness is yet upon him.
This cleansing was only required for priests but in the kingdom program the nation was such that each Jew was a priest; a "kingdom of priests".
The word translated "answer" and "response" and "examination" and such has two general usages:
ἐπερώτημα, ατος, τό (s. prec. entry; Hdt. et al.; ins, pap; Da 4:17 Theod.; Just., D. 45, 1).
① the content of asking, question (Hdt. 6, 67; Thu. 3, 53, 2; 3, 68, 1; Sir 33:3 v.l.; Just., D. 45, 1) ξένον ἐ. strange question PEg2 64. λαλεῖ αὐτοῖς κατὰ τὰ ἐ. αὐτῶν according to their questions Hm 11:2.
② a formal request, appeal (ἐπερωτάω 2) συνειδήσεως ἀγαθῆς ἐ. εἰς θεόν an appeal to God for a clear conscience 1 Pt 3:21. But cp. a pledge (s. L-S-J-M s.v. 3 with pap ref.; also the vb. in PYadin 17, 38) to God proceeding fr. a clear conscience (so GRichards, JTS 32, ’31, 77 and ESelwyn, 1 Pt ad loc.); cp. also BReicke, The Disobed. Spirits and Christian Baptism ’46, 182–86; NClausen-Bagge, Eperotaema ’41. DTripp, ET 92, ’81, 267–70, argues for a liturgical ‘stipulatio’ or injunction urging the baptismal candidate to turn sincerely to God’s way.—M-M. TW. Spicq.
Arndt, W., Danker, F. W., Bauer, W., & Gingrich, F. W. (2000). A Greek-English lexicon of the New Testament and other early Christian literature (3rd ed., p. 362). Chicago: University of Chicago Press.
The context of Peter's epistle is that of suffering innocently. He begins the discussion before the mention of baptism and continues without skipping a beat after:
KJV 1Pe 3:14 But and if ye suffer for righteousness' sake, happy
are ye: and be not afraid of their terror, neither be troubled; 1Pe
3:15 But sanctify the Lord God in your hearts: and be ready always
to give an answer to every man that asketh you a reason of the hope
that is in you with meekness and fear: 1Pe 3:16 Having a good
conscience; that, whereas they speak evil of you, as of evildoers,
they may be ashamed that falsely accuse your good conversation in
Christ. 1Pe 3:17 For it is better, if the will of God be so, that ye
suffer for well doing, than for evil doing. 1Pe 3:18 For Christ also
hath once suffered for sins, the just for the unjust, that he might
bring us to God, being put to death in the flesh, but quickened by the
Spirit: 1Pe 3:19 By which also he went and preached unto the
spirits in prison; 1Pe 3:20 Which sometime were disobedient, when
once the longsuffering of God waited in the days of Noah, while the
ark was a preparing, wherein few, that is, eight souls were saved by
water. 1Pe 3:21 The like figure whereunto even baptism doth also now
save us (not the putting away of the filth of the flesh, but the
answer of a good conscience toward God,) by the resurrection of Jesus
Christ: 1Pe 3:22 Who is gone into heaven, and is on the right hand
of God; angels and authorities and powers being made subject unto
him. 1Pe 4:1 Forasmuch then as Christ hath suffered for us in the
flesh, arm yourselves likewise with the same mind: for he that hath
suffered in the flesh hath ceased from sin; 1Pe 4:2 That he no
longer should live the rest of his time in the flesh to the lusts of
men, but to the will of God. 1Pe 4:3 For the time past of our life
may suffice us to have wrought the will of the Gentiles, when we
walked in lasciviousness, lusts, excess of wine, revellings,
banquetings, and abominable idolatries: 1Pe 4:4 Wherein they think
it strange that ye run not with them to the same excess of riot,
speaking evil of you: 1Pe 4:5 Who shall give account to him that
is ready to judge the quick and the dead. 1Pe 4:6 For for this cause
was the gospel preached also to them that are dead, that they might be
judged according to men in the flesh, but live according to God in the
spirit.
Peter is highlighting that those who suffered innocently were in a unique position to win the lost:
Noah preached to the lost for 100 years.
Jesus, when crucified went and preached to the angels in prison.
his fellow faithful Jews stand out in their separation from wicked behavior
In the middle of this discussion of the testimony of suffering innocently he says that their water baptism saves them, not by directly washing away filth (like the red heifer water) but by their participation in the repentant, suffering community in the midst of a hostile world, to whom they testify:
1Pe 3:8 Finally, be ye all of one mind, having compassion one of
another, love as brethren, be pitiful, be courteous: 1Pe 3:9 Not
rendering evil for evil, or railing for railing: but contrariwise
blessing; knowing that ye are thereunto called, that ye should inherit
a blessing. 1Pe 3:10 For he that will love life, and see good days,
let him refrain his tongue from evil, and his lips that they speak no
guile: 1Pe 3:11 Let him eschew evil, and do good; let him seek
peace, and ensue it. 1Pe 3:12 For the eyes of the Lord are over the
righteous, and his ears are open unto their prayers: but the face of
the Lord is against them that do evil. 1Pe 3:13 And who is he that
will harm you, if ye be followers of that which is good? 1Pe 3:14
But and if ye suffer for righteousness' sake, happy are ye: and be not
afraid of their terror, neither be troubled; 1Pe 3:15 But sanctify
the Lord God in your hearts: and be ready always to give an answer to
every man that asketh you a reason of the hope that is in you with
meekness and fear: 1Pe 3:16 Having a good conscience; that, whereas
they speak evil of you, as of evildoers, they may be ashamed that
falsely accuse your good conversation in Christ. 1Pe 3:17 For it is
better, if the will of God be so, that ye suffer for well doing, than
for evil doing. 1Pe 3:18 For Christ also hath once suffered for
sins, the just for the unjust, that he might bring us to God, being
put to death in the flesh, but quickened by the Spirit: 1Pe 3:19 By
which also he went and preached unto the spirits in prison;
So in Peter's view as they suffer before a hostile world they have grounds to appeal to God to save them:
Heb 6:9 But, beloved, we are persuaded better things of you, and
things that accompany salvation, though we thus speak. Heb 6:10 For
God is not unrighteous to forget your work and labour of love, which
ye have shewed toward his name, in that ye have ministered to the
saints, and do minister. Heb 6:11 And we desire that every one of
you do shew the same diligence to the full assurance of hope unto the
end: Heb 6:12 That ye be not slothful, but followers of them who
through faith and patience inherit the promises.
2Ti 2:7 Consider what I say; and the Lord give thee understanding in
all things. 2Ti 2:8 Remember that Jesus Christ of the seed of David
was raised from the dead according to my gospel: 2Ti 2:9 Wherein I
suffer trouble, as an evil doer, even unto bonds; but the word of God
is not bound. 2Ti 2:10 Therefore I endure all things for the elect's
sakes, that they may also obtain the salvation which is in Christ
Jesus with eternal glory. 2Ti 2:11 It is a faithful saying: For if
we be dead with him, we shall also live with him: 2Ti 2:12 If we
suffer, we shall also reign with him: if we deny him, he also will
deny us: 2Ti 2:13 If we believe not, yet he abideth faithful: he
cannot deny himself.