Frost and Langer carded 6-under-par 66s in the final round, overtaking Mark Calcavecchia, who had come into the day with a four-stroke lead.
Frost and Langer finished regulation knotted at 8-under 206.
They both parred the first extra hole, but Frost rolled in a birdie putt on the next. Langer couldn't match him, coming up short on a try from the rough on the par-four 18th hole.
Calcavecchia stumbled to a 2-over 74 and finished two strokes behind the leaders.
Tommy Armour III carded a final-round 5-under 67 to slip into fourth place at minus-3.
Kirk Triplett (69) and Willie Wood (70) tied for fifth at 2-under.
Notable deaths of 2014 [PHOTOS]