McIlroy overcame an early double-bogey to card two-under-par 70 in a testing breeze at TPC Sawgrass.
A tap-in birdie at the par-five 16th gave him the lead and he parred the final two holes to finish at 16-under 272.
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With Furyk already in the clubhouse after a gimme birdie at the final hole, the 29-year-old McIlroy knew what he had to do as he played the final three holes.
He used his power to reach the par-five 16th in two shots and a tap-in birdie gave him the lead.
McIlroy then safely negotiated the water-lined final two holes with tap-in pars to clinch the most prestigious tournament outside the four majors.
He will head to the Masters next month brimming with confidence. McIlroy needs a victory at Augusta National to complete the grand slam of all four modern majors.
After close calls in every tournament he had contested this year, McIlroy seemed sanguine after finally closing the deal.
"It's very special," he told Sky Sports.
"I just tried to treat it like another day, even though I've had all those close calls this year.
"If anything they were good for me. All those experiences this year led me to this point and ultimately they were good for me because they got me over the line today."
Furyk shot 67 for second place on 15-under, with Englishman Eddie Pepperell (66) and Venezuelan Jhonattan Vegas (66) another stroke back in a tie for third.
"There's a little disappointment, thinking maybe I played well enough to win," Furyk said. "Rory obviously felt differently."
McIlroy said the tough conditions had helped him remain patient on a day when a northerly wind finally helped the course bare its teeth.
He showed his maturity after hitting his second shot into water at the par-four fourth. He dropped two shots but his head did not drop.
"Any time I looked at the leaderboard I was pleasantly surprised I hadn't fallen two or three shots behind," he said.
"That gave me a little bit of encouragement to keep going and play a great back nine.
"I am just thankful that it was my turn this week."
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