Toms rebounded from a disastrous third round in which he blew a seven-shot lead to finish at 15-under 265, one stroke better than third-round leader Charlie Wi (69).
Toms racked up his first triumph since the 2006 Sony Open. He lost in a playoff to K.J. Choi last week in The Players Championship.
Toms carded an eagle from 83 yards out on the par-five 11th hole, taking the lead for good. After a 17th-hole bogey, he saved the tournament with a final par at the 18th.
Wi got to within a shot thanks to two clutch putts but came up a bit short at 14-under 266.
Bo Van Pelt (65) collected a third-place finish at minus-10 and defending champion Zach Johnson (65) came in fourth at 9-under 271.