Bob Gilder stands alone in second place at 9-under-par 133 after a 4-under 67. Bruce Fleisher, Walter Hall and Tom Watson share third place at 6-under-par 136.
Stadler rolled in a birdie at the par-4 fourth at Oak Hills Country Club to create a four-way tie for the lead early in the round. He and Fleisher burst out of the pack with birdies on the fifth and sixth to move to 7 under.
Fleisher dropped a shot at the seventh to give Stadler the lead all to himself. Stadler maintained his one-shot lead with pars on the eighth and ninth.
The Walrus sank a 10-footer for birdie on the 10th to briefly take a two-shot advantage. However, Gilder birdied the same hole to get to minus-7 and within one of Stadler.
Stadler's lead moved back to two strokes when he drained a 20-footer for birdie on the 12th. He climbed to 10-under with a kick-in birdie at the par-3 14th.
After pitching out of the trees, Stadler ripped his third shot to the par-5 15th to 25 feet. He calmly made that putt to move to 11 under, which gave him a three-shot cushion as Gilder as birdied the hole.
'I did drive the ball well except for the one on 15,' said Stadler, who has two wins in his first 12 Champions Tour starts. 'Then I chipped it out and hit a real solid 2-iron third shot. And obviously I made a good putt.'
Stadler's drive off the 16th tee found the left rough and he was forced to pitch out again. That led to a bogey dropping him to minus-10. Gilder birdied the hole to get within one shot.
'I tried to cut it around the corner Friday and clipped the trees and almost put it out of bounds. Today, I tried to hit just left of the fairway bunker, but pull-hooked it and made five,' said Stadler of his travails on No. 16. 'Tomorrow, I might just hit 8-iron off the tee and 5-iron in. It can't be any worse.'
Stadler found the fairway off the 17th tee, but his ball came to rest in a divot. Not to worry, as he muscled his second shot out of the bad lie within one foot of the cup for eighth birdie of the day. He closed his round with a two-putt par at the par-3 closing hole.
'I hit a 2-iron off the tee and unfortunately it ended right in the middle of a divot,' Stadler said of his tee shot on 17. 'I had a nice soft 8-iron, it came out perfect and I got a good bounce and I'm in there for a kick-in birdie.
'Those are the things though, the 2-iron on 15 and the shot out of the divot on 17. You have to do that stuff to shoot 64. It's little things like that, that make scores go down.'
Stadler, with a win tomorrow, would become the first three-time winner on the Champions Tour this season.
Gilder began the day one stroke behind overnight leader Jim Thorpe. Gilder bogeyed the third, but responded with back-to-back birdies from the fourth. He later matched Stadler with birdies on the 10th, 15 and 16th.
'It seemed like I was playing out of the rough all day today,' said Gilder. 'I was able to manage it well enough and make some birdies out there.
Gilder has finished second here two straight years and knows tomorrow will be tough to win.
'I've got to shoot a low number,' said Gilder. 'You know Stads is going to. He's making putts right and left. He made bogey in the end there and fired it right in there for another birdie. He's going to be tough to beat.'
Thorpe stumbled to a 1-over 72. He shares sixth place with Jim Ahern (68), Larry Nelson (67), Bill Rogers (69) and Fuzzy Zoeller (70).
Hugh Baiocchi, Allen Doyle, Hale Irwin, Tom Kite, Gil Morgan and D.A. Weibring are tied one stroke back at minus-4.