Stadler, son of 1982 U.S. Masters champion Craig, carded a one-over-par 72 in testing conditions to record a nine-under total of 204.
The 35-year-old, who has been in front since day one, is four ahead of Thailand's Thongchai Jaidee (69) and Frenchman Victor Riu (73).
Thongchai was one of only 10 men to go under par as winds gusting up to 48-kph made life difficult for the players at the venue for the 2018 Ryder Cup.
U.S. Open champion Martin Kaymer (70) of Germany was fourth, six shots off the pace.
"I got what I deserved today," Stadler told reporters. "I didn't play that great but I made a few nice up and downs for pars.
"It was just about holding it together today, I knew I didn't have to do anything crazy to stay ahead. A couple less shots would have been nice but overall I'm happy the way it went."
(Reporting by Josh Reich, editing by Tony Jimenez)
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