A final round 65 allows him to finish three shots ahead of Ben Hogan.
Bauer went on to shoot 87-79 for a total of 311 to finish 12 shots behind Rawls.
The Welshman, ranked third in the world, finished three shots off the lead on a day that saw heavy rain halt play early.
The two leaders finished 12 shots ahead of the field by finishing 12 under par over the three rounds.
However, he fell away over the weekend and ultimately finished 13 shots off the pace, in a tie for 32nd place.
I'm trying to figure out how I finished only three shots behind him.
He finishes in second place two shots behind winner Raymond Floyd.
But he scored a 2-under 70 on this year's final round and finished four shots behind the three tied for first.
He finished 11 shots behind Mickelson and left a bundle of missed putts in his wake.
Retief Goosen had a 73 and finished 16th, seven shots behind the leader.
