Reed held a one-shot lead with two holes to play after holing out from 100 yards from a fairway bunker for an eagle at the 15th and carding his fifth birdie of the day on the next.
However, the world number 17 bogeyed the 17th and left a birdie putt short from 12 feet on the 18th, tapping in for par before throwing his ball into the lake surrounding the green.
That left Broberg, who began the day two off the lead, with a birdie putt from similar range to move ahead - but he also left it short.
Jaidee and An - the final pair - both missed chances to join the play-off.
Broberg and Reed returned to the 471-yard 18th, where the American found thick rough off the tee, a greenside bunker with his approach and splashed out to four feet.