Mediate's 4-foot birdie putt came after Tom Pernice Jr. missed a 5-footer at No. 18 that could have forced a playoff.
Mediate started the day with a three-shot lead, lost it by the 14th hole, but regained it when Pernice bogeyed the par-4 17th from a greenside bunker. Mediate protected that lead with a birdie on the par-5 closing hole.
Pernice, who had a final-round 70, finished tied with Bernhard Langer (68) for second place. It was Langer's fourth top-three finish in this event in the past five years. Langer won here in 2010.
Mediate won six PGA Tour titles and also lost a memorable playoff to Tiger Woods in the 2008 U.S. Open at Torrey Pines. Mediate shot a course-record 61 in the second round on Saturday.
Mark O'Meara (69) and defending champion Corey Pavin (69) were both six shots off the lead.