Harrington, three times a runner-up on the tour, finally achieved his breakthrough after sinking a four-foot putt for par on the 18th hole while Fijian Singh missed from two feet.
Singh, Harrington and Joe Ogilvie finished the regulation 72 holes on the Sunrise course level at 14-under-par 274. The American was eliminated on the first hole of the playoff after finding a fairway bunker with his drive.
"I thought it (Singh's putt at the second playoff hole) was a gimme," world number eight Harrington said at the Country Club at Mirasol in Palm Beach Gardens. "It was a shock.
"I was mentally prepared to go back to the tee. It was a surprise...it took me a couple of seconds for it to sink in because I was really focused," he told reporters after becoming the first Irishman to win a PGA Tour event.
Singh, who has a 5-1 record in playoffs, had an opportunity to end the suspense on the first extra hole but watched his 15-foot putt roll beyond the cup in the Florida twilight.
"I'm a little disappointed," said Singh, who lost the world number one ranking to Tiger Woods last Sunday. "I hit the putt a little too hard, you can't miss putts like that in a playoff.
"I played well, I struck the ball well and could have made one or two more putts out there, but I made the ones that counted.
Harrington beat his previous best round on the PGA Tour by two strokes when he fired a nine-under 63. Singh shot a closing 64 while Ogilvie had a 68.
A frenzied final day began with Harrington seven off the lead in a tie for 21st place and with seemingly little chance of victory.
Inspired after watching South Africa's Ernie Els erase a similar final-round deficit to capture the Qatar Masters, the 33-year-old Ryder Cup player from Dublin mounted a furious charge with birdies on 10 of the first 13 holes.
He briefly let it slip with bogeys at 14 and 15 before getting back on track with another birdie on 17.
"I watched the golf from Doha this morning and saw Ernie come back and thought, why not?," said Harrington. "It gave me some confidence that, yeah, it can be done.
"The last thing you want to do out there is play it safe, so I really wanted to go at it the last couple of holes.
"It's very good to be the first Irishman. It does mean a lot to me now that I've done it.
"I wouldn't have liked to have put it up there beforehand, but now that I am the first, nobody can take it away from me."
Pat Perez finished in fourth spot on 275, with David Toms a further stroke back in fifth. Brad Faxon, Brett Wetterich and Australia's Geoff Ogilvy were joint sixth on 277.