McDowell was four shots behind when the round started, but rallied with a closing 69 over wind-blown Harbour Town Golf Links. The 2010 U.S. Open champ had his only bogey of the day on the 72nd hole to force a playoff with Simpson, the reigning U.S. Open titleholder.
McDowell struck his approach on the extra hole about 15 feet away and two-putted for par. Simpson could not answer, missing about a 10-footer for par.
Luke Donald and Kevin Streelman tied for third.
McDowell's win ended a tough day in which only three players shot in the 60s.
Donald shot a 69 while Streelman had a 72. Jerry Kelly rounded out the top five after his even-par 71.
Charley Hoffman, the 54-hole leader, ballooned to a 77 and fell into a tie for sixth.
Both McDowell and Simpson had the chance to win on the 72nd hole. McDowell missed a 12-foot par putt after his approach went over the green. It was his only bogey on the round.
Simpson had a 22-footer for birdie a short time later on the 18th, but sent it 3 feet past to lead to the tournament's third playoff in four years.
McDowell patted Simpson on the back after the playoff miss and smiled widely as the boats in Calibogue Sound tooted their horns and whistles.
Neither McDowell nor Simpson made the cut a week ago at the Masters, yet bounced back in a big way at Harbour Town.
The course showed its teeth, winds arcing flagsticks and blowing debris on every hole. Donald backed off his putt on No. 7 when a large leaf tumbled through his line. Crews watered several greens between groups simply to keep balls holding instead of skipping off the wind-swept sod.
Blowers were heard throughout the day, trying to push off leaves, twigs and other tree parts falling everywhere on the course.
The National Weather Service issued a wind advisory for the area, warning of winds of 20-to-30 mph and gusts up to 45 mph.
"Extremely difficult," Donald said of conditions. "Strongest wind I've played in all year."
Few managed the wind better than McDowell, who lurked behind most of the round until striking on the back nine. He made a 28-foot birdie putt on No. 11 to move into a three-way tie for first with Simpson and Hoffman.
McDowell broke the tie on the 16th hole, landing his approach within 8 feet and making the birdie putt. He saved par from the back of the green on the 17th hole, but couldn't do it a second time on the closing, lighthouse hole at No. 18 for his first bogey in 32 holes to fall back into a tie with Simpson.
Simpson's chase appeared over when he made three bogeys in a six-hole stretch to fall two shots behind. He steadied himself with a birdie on No. 12 and parred his way to the finish to reach the playoff.
Donald, who's got two seconds and a third in his past four appearances at Harbour Town, got an early charge going before Hoffman and Simpson hit the course with four birides on his first six holes to draw within two of the lead.
Donald, ranked No. 6 in the world, couldn't keep the surge going, though. He had birdie chances on the final three holes of the front nine, but came up empty. Bogeys on the 13th and 15th holes end Donald's run. Still, it was the fourth top-five finish in the last five trips to the RBC Heritage for Donald.
DIVOTS: Brandt Snedeker went from last off at Augusta National to first off at Harbour Town. Ranked No. 5 in the world, Snedeker's week ended early Sunday as his was the first group off the tee for the final round. He shot a 74 and did not break par at Harbour Town. Snedeker was tied for the lead last Sunday and in the final group at the Masters. ... Defending champion Carl Pettersson drifted down the leaderboard since an opening-round 68. He finished tied for 40th at 1-over par. ... Former RBC Heritage champ Jim Furyk went from a 66 Saturday to a closing 78.
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