Molder sealed the victory with a six-foot birdie putt at the par-four 18th, the sixth extra hole, where Baird could only par after his drive ended up in thick rough to the right of the fairway.
The pair had finished the 72 regulation holes at 17-under-par 267, overnight leader Baird closing with a four-under 67 and Molder firing a seven-birdie 64.
American Bud Cauley, who turned professional before the U.S. Open in June, finished alone in third at 15 under after signing off with a 66 while former world No 1 Tiger Woods (68) tied for 30th.