In the playoff, Lin tapped in a 1-foot birdie putt on the second extra hole to knock off Northern Ireland's Rory McIlroy after Italy's Francesco Molinari was ousted on the first playoff hole.
Molinari found the rough off the tee and was eliminated after missing a 15-foot birdie putt.
The trio entered the playoff with matching totals of 15-under-par 265.
In the closing 18 holes of regulation, Lin shot 3-under-par 67, while both Molinari and McIlroy shot 5-under 65.
"I'm still smiling," a stunned Lin said. "This is my first European Tour win and my feelings cannot be described."
Thailand's Chawalit Plaphol (65) and Pablo Larrazabal (67) of Spain finished two shots out of the playoff at 13-under 267.
Third-round leader Oliver Wilson (71) finished in a tie for sixth despite sharing the lead with four holes left.
America John Daly closed with an 8-under 62 and finished in a tie for 17th place.