Rose and Stefani each shot 70 to finish regulation at four-under-par 280 on a course that played much tougher than when it hosted the U.
S. Open three years ago, due to firm and fast conditions and plenty of lush rough.
“I think Congressional got its reputation back after the U.S. Open,” Rose, whose 72-hole score was 12 strokes higher than Rory McIlroy carded to win the Open, told CBS television.
Rose, 33, collected $1.170 million for his sixth PGA Tour victory, and his second in this event, with his previous triumph coming in 2010 at another classic course, Aronimink near Philadelphia.
He also has won six times internationally.
“It’s great to win on a course like this because you can’t luck into it,” said the 2013 U.S. Open champion.
“I had to rely on different parts of my game all week. I was really pleased to see the PGA Tour set it up tough. It was fair but you had to play good strategic golf.
“It hasn’t been lost on me that I haven’t won for a year. It’s a huge boost confidence-wise for sure going into a major championship.”
Rose stumbled at the end of regulation. He sank an eight-foot putt to save par at the 17th hole and then got up-and-down from 30 yards for bogey at the par-four 18th after pulling his second shot from the rough into the pond guarding the left side of the green.
But Stefani, ranked 246th in the world, found the same watery grave in the playoff and could not do better than double bogey, handing Rose the tournament.
Stefani earned a consolation prize of a berth in the July 17-20 British Open, as did fellow Americans Charley Hoffman, Ben Martin and Brendan Steele.
Overnight leader Patrick Reed’s reputation as a good frontrunner took a battering when he shot 77 to finish four strokes behind.
He had won the previous three times when he led after 54 holes.
Five players were tied late on the front nine before Rose and Stefani emerged from the pack to finish one stroke better than Hoffman and Martin.
Reed was not the only contender to struggle. South Korean Noh Seung-Yul started the day equal second, but had a back nine meltdown, limping home in 43 strokes for a 79.
(Reporting By Andrew Both in Cary, North Carolina, Editing by Greg Stutchbury)