He cooled off on the back nine, shooting one over on the final six holes.
The card showed Simpson's cup-rattling, 30-foot birdie putt off the fringe of the par-4 15th hole was his eighth of the day (to go with an eagle at No. 2), and his fifth in a row.
Jordan Spieth was also among the early starters and, like Woods, sprinted up the leaderboard thanks also to a seven-under 65. He eventually cooled off with a 1-under back nine, but it was enough to move him from a tie for 68th place when the day began to almost within striking distance of the leader. They still were 11 shots behind. In the first two rounds of eight official events Woods has played this season, he's posted a combined score of 3 over par.
But at the par-three 17th, where he took a double-bogey after finding the water on Friday, Simpson brought a huge crowd to their feet in sinking a three-footer for birdie that moved him back to 19-under.
"I got to shoot something in the probably mid-60s both days to get myself up there to have a chance or something", Woods said. "I dropped a couple shots but overall, I felt like we had a great game plan and we stuck to it". To be 11-under par, it's a shame he doesn't finish it off. I think that some of the guys will probably shoot better scores than I did out there.
And with Mother's Day falling on the final day Simpson revealed he has an added extra incentive to win. "You don't really need to go into the 60s". I read what he said about the designer Pete Dye and how he tricks you off the tee. And at the same time we're saying, if he shoots 59, can you imagine how hard the setup's going to be tomorrow?
"I'm trying not to dwell there".
Woods, a two-time victor of The Players, started the day 14 shots off the pace.
It got Simpson, too, and in some ways, in a more painful fashion than if he'd just shanked one into the water (always a possibility with Webb, whose swing lends itself to a good shank now and then.) That NBC had cued up the #59watch in the bottom right of the screen didn't help matters, either. I hit a lot of good shots. His other statistics were as impressive as you'd expect: 11/14 fairways, 15/18 greens and just 27 putts. "This golf course, as humid as it is right now, these greens are going to be holding all day and I knew that going in and I knew I had to be a little bit more aggressive in there and put the ball in these sections, and I was able to do that".
The 42-year-old Woods then jagged birdies at the 11th and 12th but that was it for his charge, with a bogey at the 14th.
"I know it's 90 degrees", Hughes said.
"That wasn't that bad a tee shot there at 14 and I ended up in a spot where I had to really, I didn't have much of a shot". I didn't beat myself up and it is the first time in a while that I've realised that I can actually make three birdies anywhere in the world.
I think this is the sort of round I can take a lot of confidence from going forward.