Despite the perfect overhead conditions throughout the final round, the tough set up had nearly every one of the field battling, with only six of the 66 player field able to break par on day four.
Argentinean Andres Romero recorded a round of three under 68 and improved 27 places highlighting the difficulty so many were having.
Rose, however, was one of those able to break par, his round of 70 securing him a spot in the playoff against Stefani who had yet to win on the PGA Tour.
The par four 18th, one of the toughest finishing holes on the PGA Tour schedule, was the first playoff hole and although both found the rough from the tee Stefani had a near impossible shot if he was to find the green.
He tried to produce that impossible shot and found the water short and left of the green and eventually too double bogey while Rose was able to par and win.
He has now proven on several occasions that he is the man for the moment when the golf courses are at their most demanding. The Englishman will now move back inside the top ten and likely to 8th position in the world ranking.
Rose will now head back to the UK for a few weeks, his next outing at the Scottish Open in two weeks time followed by what now must be a good opportunity to win his second major and his first Open Championship.
The playoff pair finished one shot ahead of Ben Martin and Charley Hoffman with Andres Romero, Brendan Steel and Brenton Todd sharing 5th position.
Four places at the Open Championship were up for grabs this week for the leading four players and ties finishing inside the top twelve but not already exempt. Stefani, Hoffman, Steele, Romero and Martin were those players. Rose and Todd were already exempt.
Marc Leishman did best of the Australians, in fact he had a share of the lead before bogeys at the 8th and 9th set him back and on the tough layout he was unable to recover. Leishman would, however, finish in a share of 8th and take his season earnings to more than US$1.4 million.
Steven Bowditch was the next best of the Australians when he tied for 1st, Brady Watt did well to finish 24th, Greg Chalmers was 30th while Geoff Ogilvy and Oliver Goss were 55th.
The PGA Tour will now play the Greenbrier Classic in White Sulphur Springs in West Virginia.