Bernhard Langer, 63, winner of green jackets in 1985 and 1993 finished 36 holes on three-under par 141 after completing a four-under par 68 first round and a second-round 73.
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.
Fred Couples and Bernhard Langer briefly turned back the clock during round two of the Masters.
Fred Couples, trying to become the oldest champion in major golf history at age 52, fired a five-under par 67 on Friday to share the lead after the second round of the 76th Masters.
Angel Cabrera and Carl Pettersson were home and dry in the clubhouse on seven-under 65 on Thursday, heading the leaderboard as thunderstorms stopped play at the US PGA Tour Houston Open.
Bill Haas got another big payoff on Tuesday when he was picked for the US team at the Presidents Cup. US captain Fred Couples used his two picks on Tuesday on Tiger Woods and Haas, who won a sudden-death playoff to claim the Tour Championship for his first win of the year.