The American held a one-shot lead after a flawless opening 64 and extended his advantage to three shots following a second-round score of 68, despite carding a double-bogey seven on his final hole.
The world No 62 suffered some frustration yesterday too when he could only manage a one over-par 72, although the wet and windy conditions meant he still finished the day four ahead of France's Victor Riu and Thailand's Thongchai Jaidee. US Open champion Martin Kaymer is six strokes off the lead after a 70. Scots Stephen Gallacher and Scott Jamieson are among seven players sharing 12th place -nine shots off the lead - after 74s.
"Since the first day he's running away a little bit, so I guess he likes the golf course as much as I do," Kaymer said of Stadler, who won his first PGA Tour title in Phoenix in February. "So I think it will be difficult to catch him.
"If the weather stays like this, I just need to shoot a very, very low score [today]. If you get within two or three shots of him, he might get some nerves the last three or four holes because it's a tough finish. But the way he plays golf and the way I know him, he's a very laid-back guy so it will be difficult to catch him."
Stadler carded one bogey and eight pars on the front nine to allow Riu to claim a share of the lead when he recorded his second birdie of the day on the ninth. At that point the 29-year-old from Paris was the only player in the field not to have dropped a shot, but a bogey promptly arrived on the 10th after he drove into the water. Stadler holed from 10 feet for birdie and a two-shot swing.
Riu holed for a birdie on the 11th but five bogeys and a birdie in the next six holes derailed his round, with his only par of the back nine coming on the 18th. Stadler remained far more consistent despite being assailed by a back injury which flared up during his round.
"It's been a little out of whack all week," acknowledged the 34-year-old. "I'm still able to swing so should be fine. Overall I'm happy with the way it went."
There is likely to be some satisfaction too for Scotland's Sally Watson, who had a share of seventh going into the final day of the ISPS Handa Ladies European Masters in Buckinghamshire. Compatriot Vikki Laing was 11th, eight strokes behind leader In-Kyung Kim of South Korea.