Woods won for the third time this year, and the 68th time on the PGA Tour, living up to his hopes of being a "greedy host" at his own tournament.
He goes to the top of the PGA Tour money list and the FedEx Cup standings for the first time this year. Woods has won all three tournaments this year in his final start before a major, with the British Open next.
Mahan tied the course record with 62 and finished alone in second. Anthony Kim, who started the day tied with Woods, finished in third at 9-under.