First, the corresponding "this" in the beginning of the quoted passage is Noah's Ark and the events surrounding it. Peter is saying that just as Noah was saved from the flood via his ark, so now it is Baptism that "now saves you." BUT before we focus on that I hope that you will answer a couple of questions.To which I say (and have already said in the meta):
1.) Is the "appeal to God for a good conscience" necessary for salvation?
2.) Is there a means, apart from Baptism, to make an "appeal to God for a good conscience?"
 Yes. The thief on the cross apparently made one, unless you would argue he did not get saved by Christ.
Kobra's problem is that he thinks that the appeal in baptism is the sine qua non -- that without which there is nothing, for those of you who didn't have the Jesuits torture you with Latin in H.S. -- and that one can make that appeal for someone else. The text here, however, makes it clear that it saves "you" because "you" make an appeal to God.
I have to admit that this passage speaks of baptism in the highest terms -- higher, in my view, than the correspondence to Noah. And here's what I mean by that, From 1 Peter 3:
- For Christ also suffered once for sins, the righteous for the unrighteous, that he might bring us to God, being put to death in the flesh but made alive in the spirit, in which he went and proclaimed to the spirits in prison, because they formerly did not obey, when God’s patience waited in the days of Noah, while the ark was being prepared, in which a few, that is, eight persons, were brought safely through water. 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 good conscience, through the resurrection of Jesus Christ, who has gone into heaven and is at the right hand of God, with angels, authorities, and powers having been subjected to him.
After he concludes his subordinate flourish, which expounds on what Christ did for us and also for those who were even disobedient to Noah, he then says, "Baptism corresponds to this". And I would be willing to admit that almost all readers of this passage think the "this" refers to "the saving in the ark". But that makes the antecedent of "this" the subordinate issue which Peter was talking about rather than the main issue which Peter was talking about -- which is the death and resurrection of Christ.
Peter is saying here that Christ suffered and died, and was raised from the dead, and now baptism corresponds to Christ's work -- showing we have died and have been raised to new life, not as a washing away of dirt but as a plea for a new conscience.
This is a much higher expression of what we mean in baptism, but ironically it is the correspondence view of the work itself: baptism is not the work of Christ, but it corresponds to the work of Christ, and shows the work of Christ.
I am more than willing to admit that baptism saves as it corresponds to Christ's work. But Kobra has to admit that it speaks of baptism in which the believer interacts with God.
Our friendly adversary Patrick Kyle has pointed out that "this" here is actually a referent to the "water" in the previous passage by virtue of Greek Grammar. He is 100% correct, so insofar as you can detach that from what I said here and still have what I said here make any sense at all, do so. We don't anathemtize posts here, but we do offer corrections whem we make mistakes, so note my mistake and more on.