Wiebe carded birdies on three of the final four holes in Friday's second round to go to 5-under 135 for the tournament.
Langer also got hot after making the turn at Royal Birkdale. After a bogey on the sixth hole, Langer birdied No. 8 and made up further ground on the 13th, 15th and 17th holes.
Langer and Wiebe are one stroke ahead of David Frost (68) and three ahead of a trio tied for third.
Thursday's leader, Gene Sauers, shot 70 Friday and was tied for fourth at 137 with Mark McNulty (67) and Peter Fowler (68).
Defending champion Fred Couples shot a 72 Friday and was 6-over 146 after two rounds.
Langer led last year's Open at Turnberry by one stroke at the start of the final round but stumbled to a 75 and finished sixth.