Perry fired a three-under 68 at Bellerive Golf Club to move to 10-under 203 for the tournament, two clear of fellow American Jay Haas (67) who is in second at eight-under.
Russ Cochran (71) holds outright third at seven-under with Canadian Rod Spittle (67) fourth at six-under.
Australian Peter Senior (69) and Japan's Kohki Idoki (68) remain in the mix in a tie for fifth at five-under.
The 52-year-old Perry, who twice lost in playoffs in golf's regular major championships, has his chance to atone on Sunday.
The Kentucky native has two previous wins on the Champions Tour for those over 50 but is yet to win a major.
His third round proved a rollercoaster with five birdies, an eagle and four bogeys.
The overnight co-leader with Cochran, Perry kicked clear with a birdie on the second and eagle on the fourth holes.
But he followed with back-to-back bogeys, rebounded with back-to-back birdies but then bogeyed the ninth to open with a 34.
He came home in the same score but in much more uneventful fashion, with just two birdies and a bogey.
Haas, a two-time Senior PGA winner and three-time Champions Tour major winner, powered back into the mix with a round of five birdies and just the lone bogey.
Cochran, who won the 2011 Senior Open Championship, appeared set to fall out of contention when he was two-over on his round through 10 holes but battled back with two closing birdies to stay in reach.
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- Russ Cochran