The Australian shot a five-under 67 to tie Langer and lead by one in a crowded leaderboard at Rancho Mirage in California.
Percy was going along merrily at six-under with birdies on the second, fourth, ninth, 10th, 11th and 14th holes when he came unstuck.
He made bogey on the par-four 16th to drop back to five under before slipping up again on the next hole, where he gave up another stroke.
But the Victorian regrouped, and with a slice of luck, chipped in on the par-five closing hole to make birdie.
"It's really hard. You've got to pick your shot, and if it goes through the wind you're in all sorts of trouble," the 50-year-old said.
"Luckily for me, I drove it well and I was hitting fairways so that made a huge difference."
Langer, meanwhile, shot his age once again and with Percy holds a one-shot lead over the trio of Jason Caron, Thongchai Jaidee of Thailand and Australian Richard Green.
Langer, 67, has already shot or broken his age three times this season. Friday's round, a bogey-free loop with five birdies, was his 27th time achieving the feat on the PGA Tour Champions.
"I hope to inspire other people," Langer said. "Some say, 'Oh, I'm too old, I can't get any better anymore.' I still think in your 50s you can still improve, maybe even into your 60s depending on what level you're playing at because golf is very technical.
"Obviously I'm a lot shorter now and I can't keep up with the young guys, but it's very technical, it's very mental and a lot of it is short game where you don't need strength, you just need great touch."
Langer and the rest of the field dealt with the challenge of strong, swirling winds.
"Hit some decent shots and didn't have to scramble too much," he said. "Had a nice bunker shot on 17, hit the flag; that might have gone a few feet by otherwise. Had a good chance on 18 to go six under and didn't make it. Very solid day."
While Langer has won a record 47 times on the PGA Tour Champions, Percy is in the hunt for his first title. He made most of his career in Australia and had one win on the Web.com Tour (now known as the Korn Ferry Tour).
Australian Steve Allan, Stephen Ames of Canada and Chilean Felipe Aguilar are tied for sixth at three-under 69, with another Aussie Stuart Appleby a stroke back in tied ninth.