Spaniard Garcia shared the lead on 13-under with Woods when he teed off at the short but treacherous 17th, but hit into the water twice to crash to a quadruple bogey, after the world number one had parred the famed island hole.
The 2001 champion Woods parred the 18th to complete a two-under 70 for a 13-under total of 275, surviving a late challenge from Sweden's David Lingmerth at the Stadium Course at TPC Sawgrass.
The impressive rookie Lingmerth missed a monster putt to bogey the last hole for a 72, and finished tied for second with Americans Jeff Maggert (70) and Kevin Streelman (67).
Garcia, the 2008 champion, compounded his miserable finish by finding water on the 18th to sign off with a double-bogey and plunge well down the leaderboard.
Woods had appeared in complete command, and led by two strokes before stumbling at the 14th after hooking his tee shot into the water on the left.
That set up a four-way tie with Garcia, Lingmerth and Maggert for the lead at 12-under.
"It was a tough battle. I felt like was in control of it after I birdied 12 and gave it right back at 14 with a double," said Woods after claiming his 78th PGA victory in his 300th career start.
"It was game on and anybody could win the golf tournament."
The 49-year-old Maggert, bidding to become the oldest Players winner, slipped out of contention when he hit his tee shot in the water on the way to the 17th green and Lingmerth took a step back with a bogey at the 14th.
It narrowed to a tie at 13-under between Woods and Garcia, who had exchanged some mean-spirited barbs as well as birdies and bogeys in their third-round pairing on Saturday.
After Woods parred the par-three 17th, Garcia took a bold line at the pin but splashed well short into the water.
Unbowed, he tried the ploy again and temporarily found land before the ball bounded into the drink.
"That hole has been good to me for the most part," said Garcia, whose 2008 Players title was decided at the 17th in a playoff against Paul Goydos.
"Today it wasn't. That's the way it is. That's the kind of hole it is. You've got to love it for what it is."
Lingmerth, who had missed his last five cuts prior to Sawgrass, was back in the hunt with a birdie at the par-five 16th after nearly holing out a bunker shot.
After playing partner Garcia rinsed his tee shot at 17, the young Swede also attacked the flag, and managed to stick his shot in close before missing an eight-foot birdie putt to remain one stroke behind Woods.
Lingmerth reached the green of the difficult 18th but left himself a 60-foot birdie putt to tie which he pushed 14 feet past the hole leading to a dropped shot and an 11-under finish.
The Web.com tour graduate said he was not intimidated going up against the likes of Woods and Garcia down the stretch of what is generally considered golf's fifth major.
"It was a great week overall," said Lingmerth. "(But) I'm in it to win it. I felt like I had a good couple of chances there towards the end and just didn't putt very well.
"I'm out there to do my own thing. Sergio does Sergio, and Tiger does Tiger, and I'm going to do me."
Tied for fifth place on 10 under par, three shots off the pace, were Henrik Stenson of Sweden (72), Scotsman Martin Laird (67) and Ryan Palmer (72).
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- David Lingmerth
- Jeff Maggert