Molder, 32, finally prevailed on the sixth extra hole with a birdie on the par-four 18th at CordeValle for the first victory of his career.
Final leaderboard
(US unless stated)
-17 B Molder (won on sixth extra play-off hole)
-17 B Baird
-15 B Cauley
-14 S Bertsch
-14 E Els (SA)
-13 J Rollins
Click here for collated scores
Defeat will have been especially tough on Baird, who started the day with a two-shot lead and although that had been cut in half at the midway point of the final round he was still in pole position to win his first PGA Tour event.
The American has not won in more than 12 years on the PGA Tour circuit but has made more money than any player without a victory with just over $11.9 million (£7.65million) in career earnings.