With six birdies, two bogeys and an eagle, the reigning Masters and US Open champion Jordan Spieth finished 36 holes on 11-under 133 to join fellow Americans Bill Haas and Jimmy Walker atop the leaderboard in the Hero World Challenge.
World number one Woods edged 41st-ranked Richard Sterne of South Africa 1 up to secure the trophy, boosting the Americans to 8-1-1 in the overall rivalry with their fifth win in a row.
Lee Westwood fired a 70 for a three-under total of 210 to lead by two from Tiger Woods, who had a 72, and Hunter Mahan, who had a 68, equalling the best round of the day at the British Open.
The American started the day with a one stroke lead, saw six different players overtake him, and then rebounded at the death to move back ahead by the smallest of margins on one-under 209.
Mahan was the first defending champion to return to the final since 2006 winner Geoff Ogilvy of Australia was runner-up in 2007.
Not to be outdone, Matt Kuchar reached the semifinals for the second time in three years with steady play, rarely taking himself out of position.
Indian golfer Arjun Atwal flirted with danger when he stumbled to a bogey on the last hole but still managed to make the weekend cut in the AT&T National here.
Olympics-bound Indian boxer L Devendro Singh continued his fine form at the International Republic of Kazakhstan President's Cup by entering the finals with a thrilling win in the last-four stage in Almaty.
Rory McIlroy is counting on some parental guidance to take his revenge on Augusta National at the Masters tournament this week.
South African Louis Oosthuizen posted a second straight 66 on Saturday to take a two-shot lead over Hunter Mahan after three rounds of the US PGA Tour's $6 million Houston Open.