Simpson took a seven-shot lead into the final round at Sawgrass, a position from which no player has failed to win in PGA Tour history.
And although the former US Open champion saw his advantage cut to four shots with eight holes remaining, a closing 73 was enough to secure a fifth PGA Tour title and the winner’s cheque of almost £1.5million.
Despite a double bogey on the last, Simpson finished 18 under par and four shots ahead of Charl Schwartzel, Jimmy Walker and Xander Schauffele, with European No 1 Tommy Fleetwood two shots further back in joint seventh.
“It feels great,” Simpson told Sky Sports. “I’m exhausted, it was a long day and it’s actually probably harder work to be ahead by five or six than near the lead. I battled through, I didn’t have my best stuff today but it was good enough.
“I tried to continue to reinforce that it’s just one shot at a time. You have a tendency to want to fast forward and get it done but I had to pace myself and stay in it.”
Woods had to settle for a tie for 11th after finding water off the tee on the 17th and making a double bogey, but the same position was good enough for Justin Thomas to replace Dustin Johnson as world No 1 as Johnson finished just a shot behind.
Woods recorded a hat-trick of birdies from the third and picked up another shot on the ninth to be out in 32, before narrowly missing from 25 feet for an eagle on the par-five 11th.
The 42-year-old tapped in for birdie and enjoyed a major slice of luck on the next after a wild tee shot hit a tree and bounced back to the edge of the fairway.
From there Woods pitched to four feet to set up another birdie and move into a tie for second place alongside Danny Lee, and the pair found themselves just four off the pace when Simpson bogeyed the 10th after missing the green with his approach.
However, Simpson responded with a two-putt birdie on the 11th and, after a drive of more than 350 yards on the 14th, Woods span his approach back off the front of the green and failed to get up and down.
“This weekend was extremely positive,” Woods, who made the cut with nothing to spare, said on Sky Sports. “I hit a lot of good shots, and it was exciting to see a few putts go in, too.
“I hit the ball better today than I did yesterday. I hit it so good... to not really mis-hit a shot today and shoot three under par is just weird.”
US Open champion Brooks Koepka had earlier equalled the course record at Sawgrass thanks to just the second albatross on the 16th in tournament history.
Koepka had already carded five birdies when he holed his second shot with a six iron from 208 yards on the par-five 16th and followed that with another two on the next on his way to a nine-under-par 63.
“It was one of those professional pushes,” Koepka admitted on PGA Tour Live. “You’re aiming a little left of the flag and you push it right on the flag and to be honest we couldn’t tell where it landed, then everybody started screaming.
“You’re not sure if it’s just because it landed close but then the roars kept going so we figured it went in. It was a helluva shot and I’ll definitely take two there.”
Martin Laird finished joint-57th on one-under after closing with a 71 for four-under.