Lee trails the trio of clubhouse leaders by just one shot after a producing a brilliant front nine in a first-round five-under-par 67 on Thursday.
Former US Open champion Lucas Glover, fellow American JJ Spaun and Colombian Camilo Villegas share top spot after starting the PGA Tour's flagship event with six-under 66s.
But Lee is hot on their heels after rolling in five birdies to reach the turn at five under before scrambling for a miracle par at the last to complete a rollercoaster back nine.
The West Australian hit a wild tee shot way right, left his second in the pine straws short of the fairway after trying to chip out and drained a 20-foot downhill putt to keep the momentum going.
Lee's only bogey of the day came after he dunked his second shot in the water on the par-5 11th hole.
Riding high after his breakthrough victory at last week's Puerto Rico Open, fellow Australian Karl Vilips had to settle for an even-par 72 after coming unstuck down the stretch.
With three straight birdies, Viilps got it to four under before dropping four shots in his last four holes, including incurring two penalty strokes.
After starting on the 10th tee, Vilips racked up a dreaded double on the par-4 sixth and compounded the blunder with bogeys on the seventh and ninth holes.
Fellow Australians Adam Scott (74) and Cam Davis (76) fared even worse, while in-form Jason Day withdrew on the eve of the tournament with an unspecified illness.
The Players' champion in 2016, Day tied for eighth at last week's Arnold Palmer Invitational.
Glover set the early pace on Thursday with four birdies in his last four holes to seize a two-shot clubhouse lead.
Enjoying a new lease of life since he switched to a long putter in 2023, the 45-year-old American benefited from a tailwind as he teed off at the par-4 18th.
The six-time PGA Tour winner then struck a nine-iron to seven feet before draining the putt to card his 66.
"There's always some really good scores and always some really bad scores around here. The margins are razor thin, akin to say Augusta or Bay Hill," Glover said.Â
Glover, best known for winning the 2009 US Open at Bethpage Black, was certainly the story of the morning as he bounced back from a birdie-bogey-bogey start after teeing off at the par-four 10th.
Spaun and Villegas matched Glover's 66 in the more difficult afternoon conditions.
World No.1 Scottie Scheffler opened with a 69 as he chases an unprecedented third straight Players' Championship win.
With AAP
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