The Rotorua Boys' High prodigy, now 27, managed birdies only on the two par 5s on the back nine. He will be in the final round today.
"It was a good, solid round [yesterday]," Lee said. "It was very windy out there. It wasn't anything like the morning guys' golf in the afternoon. I managed to stay very patient out there. I had a lot of good shots, but it was just greens getting a little bit faster [than the day before]."
Ranked an unflattering No 186, Lee had a number of birdie putts which went just past the hole, and also a number of impressive up-and-downs which meant he held par.
He said the hole locations were tough, with most meaning the golfers faced difficult slopes.
"When I missed a birdie chance, I wasn't very disappointed," he said. "I just had to make par every hole."
It's worth noting that Lee is at 204, a score that would have led the Players in all but three of the years since it moved to May in 2007.
He had started the third round equal second with South African Charl Schwartzel and American Patrick Cantlay, but five shots behind Simpson. Schwartzel and Cantlay fell away, making unusual errors with the pressure mounting. Lee kept his cool and is positioned to make a charge, especially should Simpson slip up today.
Lee had a simple philosophy about what lies ahead.
"Just got to keep my hat down and play my own game and ... I don't know, where is he at?" Lee asked.
Told that Simpson was 19 under, Lee digested that and responded: "That's an impressive three rounds, I think. It's going very, very well for him."
Too right. Simpson started with an 8-foot birdie. He holed a 100-foot bunker shot for eagle.
And that island green on the par-3 17th that ruined his bid for the record score at the TPC Sawgrass the previous day? With a front pin in the bowl, he hit a sand wedge and listened to thousands of fans surrounding the green cheer as the ball trickled down the slope to 3 feet for birdie.
It added to a 19-under 197, the score Norman had after three rounds in 1994 on a rain-softened course.
And the 32-year-old Simpson has history on his side: No one has ever lost a seven-shot lead in the final round in PGA Tour history.
"All those things that have happened, I'd love to know them if I win," Simpson said. "But I'm trying not to dwell there. I'm trying to just look forward, do what I always do on a Saturday night of a golf tournament and get ready [for today]. And that's kind of where I'm at."
Woods had his best round on the Stadium Course with a 65 despite playing the final six holes in 1 over. Spieth made two bogeys in his round of 65 as both charged up the leaderboard in the morning with big crowds and loud cheers.
They went from a tie for 68th to a tie for ninth. But they made up only three shots on Simpson and were 11 shots behind.
Dustin Johnson at least improved his chances of staying at No 1 with four birdies over his final 10 holes for a 69. He was in third place, nine shots behind.
Johnson is among six players to lose a six-shot lead in the final round.
"If you take Webb out of the equation, the golf course is playing about like it always does," Johnson said. "He's the only one that's going really low."
Jason Day, among those at 9-under 207, had a four-shot lead when he won the Players two years ago.
"The good thing about Webb is he's played well, he doesn't have to do too much out there, he has to keep it in front of him," Day said. "Don't take unnecessary risk."