Rory McIlroy continued to struggle as his slim hopes of a Players Championship defence slipped away after a scrappy level-par round left him in the bottom half of the field.
Two of his three bogeys came after finding water off the ninth and 12th tees, the second cutting short his momentum after successive birdies threatened to kickstart his back nine.
But while McIlroy, who will defend his Masters title next month, was stuck on one over, his Ryder Cup team-mates were flourishing.
Ludvig Aberg edged a step closer to the biggest individual win of his short career.
The Swede, who turned professional in June 2023 and has two Ryder Cups and three tournament victories to his name, improved his two-shot halfway lead by one after a round of 71 to get to 13-under.
Two-time major champion Xander Schauffele dropped back after a 74, Cameron Young was within three until he double-bogeyed the last in the group ahead of Aberg and Justin Thomas and Corey Conners could only manage level-par rounds of 72 to close on eight-under.
Aberg, who is local to Sawgrass, would have had a bigger advantage were it not for his second bogey of the day at the last hole, having missed a short birdie putt on 17 to open up what would have been a five-shot lead as Young was hitting it in the water down the last.
It left Michael Thorbjornsen as his nearest challenger after a 67 moved him to 10-under.
Matt Fitzpatrick was left to rue "sloppy errors" which left him six shots back in a tie for fourth.
The Sheffield golfer had seven birdies in a round of 69 but the momentum of picking up strokes at 16 and 17 was lost with a double-bogey six at the last.
Robert MacIntyre's superb seven-under round of 65 - his best at Sawgrass - had nine birdies, with a brilliant finish of three in succession from the 15th and concluding with a nerveless 10-foot par putt to get to seven-under.
World number one Scottie Scheffler shrugged off his struggles of the first two days with a bogey-free, five-under 67 to lift him to four under for the tournament.
He rejected the suggestion that the work he had been doing on the range had produced a fix for his erratic driving.
"Did I find anything? I think that would imply that I was lost, which is not the case," he said.
Seamus Power is on four-over par after a third round 74. The Waterford golfer registered five birdies on Saturday but his round was blighted by a triple bogey on the 10th and a double-bogey after finding the water on 18.
Spectators were delayed from entering the course in the morning "for operational reasons" after two people were shot and killed on Friday night less than a mile from the tournament’s main parking area and the suspect entered PGA property where he encountered tournament employees during his attempted escape.
