Funk, who became the oldest winner in event history by nearly seven years, completed the event at 9-under-par 279. With the win, he earned a five-year exemption for the PGA Tour and entrance into all four majors this year.
'I'm speechless right now,' Funk said. 'It was a tough day obviously with the wind and the conditions, but I hit the ball really good. I was in control of my swing and I felt good about that.'
The third and final rounds were both completed on Monday after serious weather problems forced the delayed finish. Players had to battle winds that gusted over 40 mph on Monday, which sent scores soaring.
The 18th hole, a par-4, yielded no birdies and played to a stroke average of 4.817 in the final round. The always difficult island green at No. 17 saw Bob Tway post a 12 in the final round after he knocked four balls in the water.
'If it's this breezy here, I don't go out. You don't even hit balls when its this windy,' summarized world No. 1 Vijay Singh, who practices at the TPC at Sawgrass regularly. 'The wind was really, really hard. We never play conditions like this. It was just brutal out there.'
Tom Lehman, the 1996 British Open champion, fired the round of the day as he closed with a 4-under 68 to share second place. He was joined at 8 under par by Scott Verplank (70) and third-round leader Luke Donald (76). Joe Durant, one of four second round co-leaders, ended in fifth at minus-7.
Funk began the final round four strokes behind Donald and was playing two groups ahead of the Englishman. Funk played his normal steady game early as he was 1 over through six holes.
The 48-year-old began to claw back into the tournament when he drained a birdie putt at the par-4 seventh. Funk made it two in a row as his birdie try at the eighth found the bottom of the cup.
Funk moved to 10 under and a share of the lead with Durant when he rolled in a 15-foot birdie putt at the 12th. The former University of Maryland golf coach converted his fourth birdie in seven holes at the 13th to move one clear.
The seven-time winner on the PGA Tour then began battling his putter. Funk three-putted for bogey on each of the next two holes to slide back into a tie for the lead with Donald and Verplank at minus-9.
'On 14, I had a brutal first putt and (at) 15 I hit a bad first putt, but both of those were really good second putts,' said Funk. 'I just hit a couple of shots on the wrong side of a hole, which you can't really help out here with the way the conditions are.'
Funk righted the ship with a two-putt birdie at the par-5 16th. He again three-putted for bogey on the island green at 17, but maintained a one-shot cushion as Verplank bogeyed the last and Donald bogeyed the 12th and 14th.
Funk, knowing he needed to at worst par the last, found the fairway off the tee. With the wind gusting from the left, he pulled his second shot into the greenside bunker left of the pin. He hit a stellar bunker shot to 5 feet and sank the par putt to enter the clubhouse at minus-9.
'It would have been nice to have a little more of a cushion there heading to the last, but I never make anything easy for myself,' Funk said.
Lehman and Verplank were already in the clubhouse at 8 under and therefore eliminated with Funk's par.
Donald and Durant had a chance to tie Funk at the last though. Durant's drive at the 18th trickled into the right rough, while Donald split the fairway.
Durant's second came up short and he needed to hole a difficult pitch to force a playoff. His chip came up well short and he eventually would walk away with bogey when he missed his 12-foot par putt.
Donald's second shot bounced right past the pin and ended up over the green on the fringe. His birdie try slid by the left edge and the crown was Funk's.
Lehman got into contention with his hot play on the front nine. He birdied four of five holes from the second to jump to 8 under. However, he played his final 12 holes at even par with two birdies and two bogeys.
'It was a very, very difficult day to play and I'm just very thankful that I was able to scramble around the golf course,' said Lehman. 'It didn't feel like I hit the ball all that great, I missed a lot of fairways, but I put the ball in the right position and made a few putts.'
Donald was done in by a 4-over 40 on the front nine of his final round. That included one birdie, three bogeys and a double bogey.
Durant, a three-time winner on tour, got off to a good start with a birdie at the second. However, it was all down hill from there as he bogeyed two of his next three holes. He finished two shots of the pace due to three back-nine bogeys.
Tim Herron and Steve Elkington shared sixth place at 6-under-par 282. Adam Scott, the 2004 champion, was one of four players one stroke further back at minus-5. He was joined there by Zach Johnson, J.L. Lewis and two-time Players Championship winner Davis Love III.
Golf's 'Big Four' - Singh, Tiger Woods, Ernie Els and Phil Mickelson - never threatened the leaders in the final round. Singh posted the best finish, a tie for 12th, at 4-under-par 284. Els finished one stroke behind the world No. 1, while Mickelson came in at plus-2. Woods posted back-to-back 75s in the final two rounds to end the tournament at plus-5.