PALM BEACH GARDENS, March 3, 2014 (AFP) - Henley rolled in his birdie putt at the par-five 18th for the victory after Northern Ireland's two-time major champion McIlroy, Scotland's Russell Knox and American Ryan Palmer had all parred the par-five that served as the decider.
Henley had parred his final three holes after a double bogey at the par-three 15th to close out a two-over par 72 and finish the tournament on eight-under 272.
McIlroy endured a difficult day at PGA National, posting a four-over 74, while Knox carded a one-over 71 and Palmer posted a one-under 69.
Despite his struggles, McIlroy had a chance to win at the final hole of regulation, where he stuck his 240-yard second shot 11 feet from the pin, but his eagle putt trickled past.
In the playoff, Henley was the only player to reach the green in two, and he two-putted from some 40 feet for birdie.
Palmer missed a 10-foot birdie attempt, while McIlroy fired out of a bunker to the front fringe and had to scramble for par and Knox missed a 20-foot birdie putt.
"This isn't going to sink in for a while," said Henley, whose bid for a second career title appeared to be over after his double-bogey five at the par-three 15th.
"I don't know what's going on right now," he added. "I'm so nervous coming down the stretch, just trying to hang in there, trying to enjoy it."
American Billy Hurley carded a 68 to finish fifth on 273. Canada's David Hearn with a 67 and American Will MacKenzie with a 70 shared sixth on 274.
World number one Tiger Woods withdrew after 13 holes citing back pain.
Woods, who had barely made the cut but came alive with a five-under 65 on Saturday, was five over for the day when he called it quits.
The 14-time major champion said he didn't yet know if he would be fit enough to defend his title at the World Golf Championships-Cadillac Championship at Doral starting Thursday.
"It's too early to tell," Woods said. "I need treatment every day until Thursday to try to calm it down. We'll see how it is."
Woods's abrupt departure was just part of the drama that unfolded on Sunday afternoon, when McIlroy opened the door but his nearest pursuers were repeatedly unable to step through it.
"Even if I had won today, it would have felt a little bit undeserved. When you go out with a two-shot lead you have to play well enough to go out and win the thing."
Both of McIlroy's birdies on the front nine were followed by bogeys, and he dropped another stroke at the ninth.
He gave another stroke back at 12 before his double-bogey at 16, where he hit out of a bunker and into the water, and his bogey at 17 cost him even a share of the lead.
Henley, who had pitched in at 14 for a second straight birdie, then lost momentum when he found the water at 15.
Palmer, playing ahead of McIlroy and Henley, bogeyed the last to fall to eight under, where Knox was the first to join him in the clubhouse.
Leading final-round scores on Sunday in the $6 million US PGA Tour Honda Classic (x-won at first playoff hole; USA unless noted; par-70):
272 - x-Russell Henley 64-68-68-72, Ryan Palmer 68-66-69-69, Russell Knox (SCO) 70-63-68-71, Rory McIlroy (NIR) 63-66-69-74
273 - Billy Hurley 70-67-67-69
274 - David Hearn (CAN) 67-70-70-67, Will MacKenzie, 67-68-69-70 275 - Sergio Garcia (ESP) 72-68-68-67, David Lingmerth (SWE) 69-68-68-70, Luke Donald (ENG) 67-68-68-72, Stuart Appleby (AUS) 69-69-65-72
276 - Andres Romero (ARG) 70-68-71-67, Matteo Manassero (ITA) 67-71-71-67, Paul Casey (ENG) 72-68-69-67, Chris Stroud 69-66-73-68, Chris Kirk 69-67-72-68, Adam Scott (AUS) 68-69-70-69, Martin Flores 69-70-68-69, George McNeill 70-67-69-70, Freddie Jacobson (SWE) 69-69-67-71, Daniel Summerhays 70-65-69-72, Keegan Bradley 69-68-66-73, Jhonattan Vegas (VEN) 70-66-66-74
277 - Nick Watney 71-69-70-67, Patrick Reed 71-67-70-69, Chesson Hadley 73-66-69-69, Gonzalo Fernandez-Castano (ESP) 71-69-68-69, Rickie Fowler 69-69-69-70, Tyrone Van Aswegen (RSA) 67-71-68-71, Brian Stuard 72-68-65-72, Luke Guthrie 67-73-65-72, Matt Every 66-73-65-73