Stadler survived a tense battle between he, Watson, Deleat, Hideki Matsuyama, Hunter Mahan, Charles Howell and others over a final nine holes that witnessed all sorts of ebbs and flows.
Watson a four time winner on the PGA Tour leading into this week appeared as if he was the man to beat until bogeys at the par 3 6th when long with his tee shot and at the 18th when again he was long with his second from an awkward angle cost him victory.
Stadler appeared to blow his chances of a first PGA Tour victory when he double bogeyed the 11th hole and struggled on the greens but a crucial two putt birdie at the 17th allowed he and Watson to play the final hole tied at 16 under.
Watson found the rough from the tee and left himself with an impossible angle to a back right flag position and finished 10 yards through the green. Despite hitting a stunning recovery to four feet he missed the putt and although Stadler missed a birdie from 12 feet his two putt par got the job done.
Stadler has now won on the European, Web.Com, South American and PGA Tours, and while still some way behind the great record of his father, Craig, he is slowly but surely developing into a player with a comprehensive career.
The European Tour title Stadler won was the Johnnie Walker Classic at the Vines Resort in Perth.
Stadler has been ably assisted in recent times by the former caddie of Australian Nathan Green, Shannon Wallis. Wallis was on the bag when Green secured the Canadian Open title in 2006.
Matt Jones shared the lead through 36 holes and although he tread water for much of today's final round he added yet another good cheque when he finished 12th. Greg Chalmers was 15th.