LONDON, July 29, 2013 (AFP) - Wiebe and Langer had been unable to finish the tournament on schedule on Sunday when bad light forced the play-off to be postponed after two halved holes.
But Wiebe won the title for the first time after three more holes on Monday morning when Germany's Langer fired a bogey on the 18th.
It was a frustrating finale for Langer, who had squandered a golden opportunity to win the title without a play-off when he produced a double-bogey on the final hole on Sunday.
The final round had been pushed well into the evening on Sunday by stormy weather in Southport, northwest England, and when Langer, who led by three shots after the opening nine holes, cracked on the last hole tournament organisers asked the players to start the play-off.
However, darkness quickly descended to bring an end to the duel in the dusk and it was Langer who stumbled once more when play resumed at 0800 local time (0700 GMT) on Monday.
It was the first time in its 27-year history that the tournament concluded on a Monday and Langer blinked first as he narrowly missed a putt for par from six feet.
Wiebe had never won a major title -- his best result was a tie for 12th place in the PGA Championship in 1989 -- and he was surprised to win the event in the manner he did.
"I'm a little tired, I'll tell you that. I was surprised that Bernie missed his putt because he's a great putter, he's a great player. It just was my time," Wiebe told Sky Sports television.
"The golf course is unbelievably demanding and whether it's a play-off or during the round.
"I have never been in a play-off in a major championship either so I was a first-timer. I just tried to play the golf course as good as I could."
Wiebe also admitted it was a unique experience to have played in near darkness on Sunday.
"I have never done that, so that was unusual but I think we would have both liked to have played (to a finish) because of our schedule," he said.
"Obviously it was really dark at that second hole and mother nature always wins.
"I just figured that this is par for the course and we will go at it again at eight and here we are."