Vegas, Woodland and defending champion Bill Haas all finished regulation tied at 27-under 333 on the Palmer course at PGA West. Vegas and Woodland each fired 3-under-par 69s and Haas carded a 6-under 66 to force a three-way playoff.
Vegas and Woodland each birdied the first playoff hole, the par-5 No. 18. But Haas was eliminated after settling for a par.
The survivors then moved on the par-4 No. 10. Vegas' drive hit a fairway water hazard but he recovered for a par. Woodland ended up in the bunker and missed a long putt for par, handing the 26-year-old former Texas Longhorn his first PGA victory.
Vegas and Woodland finished regulation knotted after also sharing the fourth-round lead.
Ryan Palmer gained sole possession of fourth place at minus-26 after carding an 8-under 64 Sunday while Brian Gay (62) and Kevin Na (67) tied for fifth one stroke further back.