Jordan Spieth (68) and Justin Thomas (70), also squeaked into the weekend, while Rory McIlroy, Hideki Matsuyama, Rickie Fowler and Phil Mickelson all missed out.
"It was a good solid round", Lee said. "If it's windy tomorrow like it was today and you're not very sharp, you're going to struggle around here". It got really windy out there in the afternoon, and it wasn't anything like the morning guys' golf in the afternoon. "I was just trying to shoot something in the mid-60s today, and managed to do it".
Lee was at 204, a score that would have led The Players in all but three of the years since it moved to May in 2007. Made birdie. 18 was a bonus to make that putt.
Simpson birdied the island green hole at 17, and that brought him to 19-under.
Not to be outdone by groupmate Tiger, Mackenzie Hughes sinks this birdie on 8.
It added to a 19-under 197, tying the 54-hole record set by Greg Norman on a soft course in March.
Someone - whether it's Woods or Spieth or someone else - will have to get rolling early and put some pressure on Simpson, a four-time victor on Tour, at golf's "fifth major".
If there were any demons from that shot lingering in this Demon Deacon's head-pardon the pun, but Simpson is a 2008 graduate of Wake Forest-he didn't let them affect him, as he spun back a wedge to three feet and made birdie.
So I've got to come out tomorrow with that same mindset that I have a few par-fives, I have a few short par-fours, and there's going to be birdie chances, so I can't force anything, even if I'm even through 12 holes.
But the 33-year-old has been coming into form with a third place alongside Louis Oosthuizen in the Zurich Classic of New Orleans followed by a top-10 finish at Quail Hollow on Sunday. "So, it shows you where it actually matters and that's on the greens".
After hitting his tee shot into the fairway bunker, Potter, Jr. hit his next to the primary rough and reached the green on his fourth shot, rolling a one-putt bogey on the 384-yard par-4 fourth. Simpson's 18-footer for a par on the last summed up his performance.
The world No 1 is one ahead of Jason Dufner, Xander Schauffele, Jimmy Walker and Jason Day, with Woods and Spieth back on eight under alongside leading English challengers Ian Poulter and Tommy Fleetwood.
"Obviously it all depends on how Webb finishes", Day said of his chances of a second Players title after his round. I felt like I was going along really nicely.
Tiger Woods, at one-under 143, was in danger of missing the cut after a mediocre 71.
An eagle and nine birdies, including six in a row from the 11th, left Simpson needing to birdie the final two holes to join the elite group of players to break the magical 60 barrier on the PGA Tour. He would play the rest of the round in one over, however, leaving a less-than-ideal taste after a round that looked like it would challenge the course record of 63.
It was his lowest round on the PGA Tour since a 65 in the second round of the Wyndham Championship at the end of the 2015 regular season.
The ball hit the wooden frame on the front of the green, caromed high in the air and landed on the back of the green with so much momentum that it rolled through the light collar of rough and disappeared into the water. It is the lowest of the 66 rounds he's played at the Players Championship, his lowest round since returning from spinal fusion surgery and his best round in relation to par since 2013. "10 to 15 feet today, and anywhere inside, which was probably the first time this year that's been the case", Spieth said, per Bob Harig of ESPN.com.
Fans should get a thrill out of watching Woods and Spieth play together Sunday. Simpson, now holds the largest lead at seven in the history of the tournament.