Langer's round of 1-over 72 enabled him to finish at 5-under 279, just good enough to edge out Corey Pavin by a single stroke at Carnoustie Golf Club in Scotland.
The German great, winner of two Masters titles on the PGA circuit, collected his first major Champions Tour victory.
Pavin ended with a 1-under 70, finishing the tourney at minus-4.
Peter Senior registered a 3-under 68 to forge a third-place tie at minus-1 with Russ Cochran, Fred Funk and Jay Don Blake, all of whom carded 72s Sunday.
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