Woods closed with a 7-under-par 65 to collect his 67th PGA Tour win at 12-under 276, a stroke better than runner-up Jim Furyk.
Woods trailed by four strokes entering Sunday's final round, but moved into a tie for the lead after seven holes. An eagle at the par-five 11th moved him one shot behind the then-leading Byrd. He shared the lead before a bogey at No. 16, but then closed strong.
Furyk made a 22-foot birdie putt on the final hole to get his fifth top-10 and second runner-up finish at the Memorial.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut