Watson found himself in further bother on the par-3 sixth, as he sent his tee-shot wide right, leaving a difficult pitch, while Cink got a fortunate bounce off a bank to send his ball to the centre of the green.
Cink managed to get down safely in two to register a second straight par while Watson produced a fantastic up and down to remain just one shot behind the 36-year-old.
Watson's challenge collapsed on the par-5 17th, however, as he carded a double-bogey 7 and Cink scored a birdie. The veteran fared no better on 18, eventually losing the play-off by a disappointing six shots.
Italian teenager Matteo Manassero secured the silver medal awarded to the leading amateur after the 16-year-old ended with a round of 69 for a total of 2-over.