Fleetwood, who won at January's Abu Dhabi Championship, shot a superb nine-under 63 to make up eight shots on Austrian Wiesberger in China.
But the 26-year-old drove into trouble on the extra hole and Wiesberger holed out from five feet for the win.
England's Ross Fisher finished joint third after a bogey on the 18th.
Fisher had seemed set to join Fleetwood and Wiesberger in the shoot-out but his error on the last left him tied with France's Gregor Bourdy on 15 under.
English duo Jordan Smith and Matthew Southgate were the next highest-placed Britons, finishing another four shots back in joint 14th.
England's Tommy Fleetwood was denied a second 2017 European Tour title after losing a play-off to Bernd Wiesberger at the Shenzhen International.