Fuzzy Zoeller, Craig Stadler, Lanny Wadkins and Hale Irwin share fourth place at 4-under-par 67.
Thorpe's round did not get off to a great start Friday as he three-putted from 25 feet for a bogey at the par-3 second. He reclaimed the lost stroke two holes later when he knocked a pitching-wedge to a foot to set up the tap-in birdie.
He closed his front nine with a six-foot birdie putt at the eighth but made his move up the leaderboard with is fine play on the back nine.
Thorpe, who won this year's Long Island Classic, reached the par-5 10th green with a 6-iron and sank the 10-foot eagle putt to go 3 under on his round.
'No. 10 was the turning point in my round,' admitted Thorpe.
He drained an eight-foot birdie putt at the 12th but played a 3-iron over the green at the 13th and missed his six-foot par save. Thorpe holed a six-footer for birdie at the 15th and made it back-to-back birdies at the 16th when he ran home a 20-footer.
Thorpe took sole possession of the lead at the 198-yard, par-3 18th. He hit a 4-iron to four feet and cashed in on the birdie putt to post his best opening-round score on the Champions Tour in 2003.
'You've got to drive the ball well here and be very precise with the iron shots,' said Thorpe. 'We have a strong field and I need to continue to make birdies the rest of the week.'
Fleisher tallied seven birdies and one bogey on his round and was tied with Thorpe for the lead when Fleisher reached the 18th tee. Fleisher used a 5-iron and missed the green short but hit a good chip to two feet. He missed the putt to make bogey and fall one behind Thorpe.
Fleisher echoed Thorpe's words on what it takes to play well at Oak Hills.
'This is a course where you've got to have patience,' said Fleisher. 'You have to put the ball in the fairway if you want to have some birdie chances. I've got to step it up if I want to stay near the lead.'
Gilder, who chipped in for birdie at the 11th, fell two behind Thorpe after he drove behind the trees at the 17th. He came back with a 15-foot birdie putt at the last to match Fleisher in second place.
'I made a few mistakes out there but I putted very well and got lucky on one chip,' said Gilder. 'If you don't hit it in the right places, you're blocked out.'
Bill Rogers and Allen Doyle share eighth at 3-under-par 68, followed by 12 players who share 10th at minus-2, including Tom Kite, Raymond Floyd and 2002 European Ryder Cup captain Sam Torrance.
Arnold Palmer bettered his age for the first time this season with a 2-over 73. Palmer, 74, is tied for 49th place with, among others, defending champion Dana Quigley.