Northern Ireland's McDowell fired a final-round 67 to finish on five under par and overnight leader Stadler needed a par at the last to force a playoff in wet and windy conditions at Le Golf National.
He narrowly failed with a birdie putt from 25 feet which would have sealed victory and inexplicably missed his next effort to card a final-round 76 and hand McDowell his 10th European Tour victory.
"I'm very surprised," McDowell told the European Tour website.
"Midway through my second glass of red wine last night, when I was very disappointed with my back-nine performance on Saturday, I really didn't think I'd be a) standing here with an opportunity to be in a playoff and b) with a trophy in my hands. "I feel very fortunate. Kevin Stadler is a great, great player. I literally gave him that putt on the last green. I didn't expect him to miss that.
"It's not really the way you like to win. I was ready to go for the playoff, but I'll take it and run. I really needed this victory. It's a special one for me. It's pretty timely. There's a busy summer ahead,"Former U.S. Open champion McDowell, who made five birdies and a solitary bogey on the last hole, trailed Stadler by eight shots after the third round and his win should guarantee him a place in this year's European Ryder Cup team.
It was the biggest comeback victory on the European Tour since Rafael Cabrera-Bello's win in the 2009 Austrian Open.
Thailand's Thongchai Jaidee finished tied with Stadler for second place and Sweden's Robert Karlsson was a shot further back in fourth.
(Reporting by Ed Osmond, editing by Justin Palmer)