Wiebe had four birdies on the back nine. Langer, the 2010 champion at Carnoustie, shot a 67 and made five birdies. Both players finished at 5-under 135.
''I really got my irons zoned in on the back nine,'' Wiebe said. ''I know there's a long way to go, but I'm tickled to be where I am. It was unbelievable and great to shoot the low round.''
Wiebe moved to 1 under by the turn with two birdies and a bogey. He had three birdies in four holes from the 13th and added another with a 15-foot putt at the last.
The German dropped two strokes at No. 6 when he double-hit the ball.
''The ball was sitting up in the long grass and I caught it high on the clubface and again on the follow through,'' said Langer, a two-time Masters champion. ''But that was my only blemish. Most of it was impressive and good, and I putted a little better today.''
David Frost of South Africa (68) finished a stroke back in third. He picked up birdies at Nos. 2, 5 and 9 to move to 5 under. He faltered slightly on the back nine, dropping shots at the par-3 12th and 14th before a birdie at No. 17.
''It was a bit of a shaky round,'' Frost said. ''I didn't feel comfortable with the club in my hand. I hit some wayward shots, but managed to hit good irons into the greens and the putter was my savior.''
Tom Watson, Frost's playing partner, only got going after a front nine featuring two birdies, two bogeys and a double bogey. The American made long putts at Nos. 11, 12 and 13 and holed another birdie at the 15th. He bogeyed the last two to finish at 4 over.
Overnight leader Gene Sauers shot a 70 for a share of fourth place with Peter Fowler (68) and Mark McNulty (67).