Rose also bogeyed the sixth hole but carded four birdies and finished with a 2-under 70 for the round and a 16-under 272 for the tournament.
The win was the fourth on the PGA Tour for Rose.
Watson, playing in the group behind Rose, had five bogeys Sunday but made a bid to force a playoff with a great approach shot from the rough that landed 9 feet from the hole. His birdie putt, however, missed and he ended the day with a 74.
Rory McIlroy shot 67 Sunday and took third at 13-under.
Tiger Woods withdrew with some tightness in his Achilles tendon after teeing of at the 12th hole.
Woods' agency issued a statement confirming his left Achilles had tightened earlier in the day and worsened during the round.
He was 3-over after 11 holes and 6-under overall when he left the course.