Molder finally took the epic playoff with a birdie on the last extra hole to beat Baird for his initial win on the tour after an up-and-down career.
He and Baird, who also was seeking his first career victory, finished regulation at 17-under-par 267.
Molder had finished in the Top 10 on 17 occasions without a win on the PGA Tour.
Tiger Woods, meanwhile, finished out of contention in his first tournament in two months. He ended in a tie for 30th at 7-under 277 after registering a third straight 68.
The match was marred when a fan threw a hot dog in the golfer's direction, although it didn't hit him. The spectator was arrested.