On a superficial level, Pi's faith contributes to his survival by providing daily ritual. On a deeper level, Pi's faith contributes to his survival through answered prayers.
Let's explore Pi's survival on the physical level first. If you look closely at chapter 63, you will see that exactly how much keeping busy with daily rituals contributes to Pi's survival. This chapter contains Pi's daily agenda. In regards to your specific question, what is the most interesting is the number of times Pi has recorded the word "prayers." Pi prays more than he does anything else on the raft. He prays no less than five times every day. Pi considers these prayers just as important as any other physical, survival preparations: "I kept myself busy. That was one key to my survival."
Now let's explore Pi's survival on a spiritual level. As a scholar of the religions of the world, I am going to suggest a deeper meaning here. Keep in mind that the deeper meaning I suggest is purely subjective (and not necessarily the opinion of the author). This is because I believe that Pi actually survives because of the deity/deities in which he calls upon. There are two instances where Pi (probably even subconsciously) calls upon these deities from the three major world religions of which he has combined: Christianity, Islam, and Hinduism. Both of these instances involve life or death situations.
Interestingly enough, the first instance involves Richard Parker's survival and the second instance involves Pi's survival (spared FROM Richard Parker).
I could see [Richard Parker's] head. He was struggling to stay at the surface of the water. "Jesus, Mary, Muhammad and Vishnu, how good to see you, Richard Parker! Don't give up, please. Come to the lifeboat! ... Swim, swim!"
Here, Pi is absolutely ecstatic to see Richard Parker. They knew each other from the zoo, of course. Pi is happy to have any creature survive with him. (In reality, even after almost a year at sea, Pi will admit that this kinship with the tiger is the very thing that kept Pi from death.) Pi's prayer is answered when Richard Parker enters the lifeboat.
The next prayer is a bit different, to say the least:
My heart stopped and then beat triple speed. I turned. "Jesus, Mary, Muhammad and Vishnu!" I saw a sight that will stay with me for the rest of my days. Richard Parker had risen and emerged. He was not fifteen feet from me. Oh, the size of him! The hyena's end had come, and mine.
Here it is Pi who is on the point of death. Richard Parker, a deadly animal, could have easily killed Pi. However, due to Pi's prayer, Pi is saved. A miraculous rat "appeared out of nowhere" that Pi is able to fling at Richard Parker who, already a bit hesitant to leap on the less than firm tarpaulin, accepts the rat as an "offering" and flops back down on the bottom of the lifeboat.