Molder outlasted Baird to finally prevail on the sixth extra hole with a birdie on the par-four 18th at CordeValle for the first victory of his career.
Defeat will have been especially galling for Baird who started today 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 US dollars 11.9 million (£7.65million) in career earnings.
Bud Cauley was third with a five-under-par 66 and 15-under-par 269 overall while Ernie Els and Shane Bertsch were a further shot back.
England's Paul Casey started today in a tie for second with Els but a poor round of 71, including three bogeys and a double bogey, saw him finish joint seventh.
Tiger Woods finished in a tie for 30th after his third successive round of 68 and he was also the target for a spectator who threw a hot dog at the American.
It was the 17th playoff this year on the PGA Tour, setting a record dating to the modern era that began in 1970.
Baird appeared on the verge of victory when he chipped in from short of the 17th green for eagle to take a one-shot lead.
Molder rolled in a 12-foot birdie putt on the 18th to close with a seven-under-par 64, which got him into the playoff with Baird shooting a four-under 67 as both finished at 17-under 267.
He twice had birdie putts on the 18th in the playoff to win, missing from eight feet and 12 feet.
Molder had three chances to win with eagle putts on the 284-yard 17th, missing from 20 feet, 15 feet and 12 feet before his winning effort on the sixth extra hole.
"It's a little surreal right now," Molder said. "That's a lot of golf today."
For Baird though it is 348 starts without victory and he said: "I finished second before four times, and only one of those four times did I really honestly think I had a chance to win.
"The other times they weren't back door seconds, but I didn't feel like I was out there to win the tournament.
"Today I felt like I was out there to win the tournament.
"For me that's a big deal," Baird said. "There's a hurdle that I overcame today that I'm not scared to talk about it."