Ernst birdied at the 18th in his final round to move to eight under alongside Lynn at the top of the leaderboard.
And the American took one hole to claim victory when the two went head to head in the play-off on the final hole.
Ernst hit the fairway with his approach, with his second landing on the green, some 15 feet from the hole.
It was in stark contrast to Lynn, whose second shot found the bunker, with his resulting chip flying across the green.
The damage was done with his second chip eight feet from the hole.
Ernst's birdie putt just evaded the hole, but the 22-year-old, whose previous best finish was a tie for 47th at last week's Zurich Classic of New Orleans, tapped in for the win
Phil Mickelson looked set to claim the title, but bogeys at 16 and 17 took him from one ahead to a shot behind before he missed a 19-footer for the birdie which would have taken him into the play-off.
Nick Watney was joint leader with Mickelson heading into the final day at eight under but a four-over 76 ended his challenge.
Rory McIlroy, who was in contention at the turn, faded in the back nine with a double bogey at the par four 12th starting a decline which saw him finish one over for the round and four shots behind Ernst and Lynn.
Lee Westwood came close but dropped shots at three, 12, 13 and 17 to undo all his good work following birdies at the first, fifth, 10th and 14th.