"God, it feels good," said Watson, whose last win, at the 1987 Nabisco Championship, was 140 tournaments ago.
David Duval, who picked up five strokes in the last five holes, took second in the pounds 1.2m event with a final-round 67.
The tournament host, Jack Nicklaus, who designed the Muirfield course, called Watson's victory "the most thrilling win in golf in the last 10 years".
Watson, 46, began the day with a one-shot lead. He bogeyed the first hole with the kind of miss on a short, three-foot putt that has characterised his play over the past several years. But he steadied himself after that.
Watson looked to be cruising as he approached the 14th hole holding a four-shot lead. By the time he looked down the final fairway, however, he was just one shot in front of Duval, who was safely inside the clubhouse.
Watson walked up the 18th to a big ovation. "If I'd had a five-shot lead I probably would have enjoyed it more than having just a one-shot lead and having to two-putt a slick 15-foot putt downhill," Watson said. He said he was trying to leave the first putt short, but the ball rolled swiftly, straight into the centre of the cup.
Jose Maria Olazabal's return to golf will not now be in this week's English Open at the Forest of Arden or next week's US Open in Michigan. Olazabal, who has not played a tournament since last September because of rheumatoid arthritis in both his feet, withdrew yesterday from both events.Reuse content