Thomas ended one shot clear of Lee Westwood, but was in danger of missing the cut on Friday before carding two birdies on the final three holes to stay in contention.
That was followed by a 64 on Saturday and a closing round that featured three birdies and an eagle between the ninth and 12th holes as he moved ahead of Westwood.
After his victory, Thomas recalled how his grandfather, who passed away last month aged 89, was at the forefront of his mind as he sealed the win
Westwood and Bryson DeChambeau, another player eying victory on Sunday, both came unstuck on the front nine of the notoriously difficult TPC Sawgrass course with Westwood shooting bogeys on the second, fourth and eighth holes and DeChambeau carding a double bogey on the fourth.
Thomas, who took home $2.7 million in prize money, now has 14 wins on the PGA Tour.
He is only the fourth player to win a major — the 2017 USPGA Championship — the FedEx Cup, a World Golf Championship event and the Players Championship.
“I was replaying what he told me a lot in my head,” said Thomas.
“He likes to give me a lot of grief, especially when he’s not here … we’re all pulling for him and I’m so glad to hear everything’s been going well with him.
“Part of me wishes he was here so I could rub it in his face a little bit more, but I’m happy and I hope he’s happy and I appreciate his help.”
DeChambeau and Brian Harman finished tied for third on 12-under behind Thomas and Westwood, while Talor Gooch and Paul Casey shared fifth place on 11-under.