Woods, who hadn't won a PGA event since the 2009 BMW Championship, ended at 13-under-par 275 and claimed the Arnold Palmer event for the seventh time in his career.
It was the first trip to the winner's circle for the former world No. 1 since a 2009 car accident that ultimately led to revelations of marital infidelity and a divorce from his wife amid a media firestorm.
Woods has also been hampered by various injuries since his return to the PGA circuit last year.
The victory was career win No. 72 for Woods, moving him to within one of Jack Nicklaus.
Graeme McDowell finished alone in second place after struggling to a 2-over 74, finishing at minus-8.
Taking third was Ian Poulter (74) at 6-under 282.
Ernie Els, who needed a third-place-or-better finish to qualify for The Masters, fell short of that goal, managing a 3-over 75 for a fourth-place tie with Brian Davis (70), Kevin Na (73), Ryan Moore (70), Bubba Watson (72), Johnson Wagner (74) and Bud Cauley (72).