Though much could be said here about Jesus being our Passover Lamb, I'll simply refer you to an article entitled "Christ in the Scriptures: Exodus and the Passover Lamb," by Stephen Sizer. It's a very detailed look at how Jesus is the fulfillment of all the Jewish Passover traditions, prophecies, hopes, and dreams.
Instead, I want to focus on the method of salvation that we find in the Passover. Were the Jews saved by the blood of the lamb that they put on their doors? No--the blood didn't save them. God saved them. Conducting a sacrifice saves no one-- the sacrifice is an act of receptivity to God's salvation that He offers, but the sacrifice, in and of itself, cannot save. The Jews were not saved by their own deeds--they were saved by the mercy of God.
Ephesians 2:4-5 says:
4 But God, being rich in mercy, because of the great love with which he loved us, 5 even when we were dead in our trespasses, made us alive together with Christ—by grace you have been saved—
And verses 8-10 say:
8 For by grace you have been saved through faith. And this is not your own doing; it is the gift of God, 9 not a result of works, so that no one may boast. 10 For we are his workmanship, created in Christ Jesus for good works, which God prepared beforehand, that we should walk in them.
In other words, the good works we do are a result of our salvation, but our salvation is by grace, through faith. Putting blood on their doorposts was a gesture of receptivity toward the salvation that God offered, but lamb's blood had no power to rescue them from the death that threatened. Nothing but the blood of Jesus can save--and the lamb's blood was simply a foreshadowing of Jesus' sacrifice that He would one day make on our behalf. In the same way, the "sinner's prayer" and baptism are gestures of receptivity toward God, but they are not works that we do to save ourselves. Only the blood of Jesus can save us, and we receive that gift by grace, through faith.
As we draw near to the season of Lent, a time of introspection, prayer, and repentance, I hope that you'll live every day by offering God gestures of receptivity toward the saving work He wants to do in your life. Nothing you can do can save you--that salvation comes only by trusting God, who can do all things. I pray you will put your trust in Him today.