Langer, who shared the lead with Corey Pavin after 36 holes, sank three birdies and made 14 pars Saturday en route to the three-stroke lead at Carnoustie Golf Club, finishing at 6-under 207.
Langer could have ended the day four shots ahead, but his drive on the 18th hole rolled about 30 yards into a bunker and he closed with a bogey.
The German great has 10 career wins on the Champions Tour but is still seeking his first major tourney title.
Pavin, meanwhile, carded a 72 to fall to 3-under 210, still good for sole possession of second place.
Fred Funk zoomed up 16 places on the leaderboard by registering a 4-under 67, joining Jay Haas (72), Larry Mize (72), Ian Woosnam (72), Jay Don Blake (70) and Russ Cochran (70) in third place tied at 2-under 211.