The closing hour was a series of blunders at PGA National, particularly by Rory McIlroy, who lost a two-shot lead by closing with a 74.
Henley was in position to win in regulation until he chunked a wedge and had to scramble for par on the par-5 18th. In the playoff, he was only player to reach the green in two and two-putted for birdie and the win.
Russell Knox, Ryan Palmer and McIlroy all made par in the playoff.
Henley, who closed with a 72, won for the second time and qualified for the Masters.
Tiger Woods withdrew after 13 holes, citing a lower back injury.
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