Saved through Baptism? (1 Peter 3:21,22)

Peter tells us, "Baptism, which corresponds to this, now saves you." This is a pretty strong statement as it sounds like this baptism actually gives us the blessings of Christ. However, Peter says after this, "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." We are those who make a pledge to God and then we are baptized. This sounds like we first profess, and then we receive baptism. However, we notice the precedent is actually quite different. Scripture actually teaches us that first someone professes, and then the household if baptized. How does Noah's flood teach us this very promise?