Even with the blemish on 17 that cost him a chance at the course record, Simpson's round was exquisite.
On the European Tour, Denmark's Lucas Bjerregaard shot 68 and Julien Guerrier a 65 to lead the Rocco Forte Sicilian Open at a wild and windy Verdura Golf Club.
Six birdies in a front nine 30 sent waves of excitement through the large gallery at the PGA Tour flagship event.
The 37-year-old needs to sneak inside the world's top 60 golfers in time for the May 21 and June 11 deadlines if he wants to avoid teeing it up in sectional qualifying.
But his astonishing performance elevated him five shots clear of the chasing pack, led by Charl Schwartzel, Patrick Cantlay and Danny Lee, while Tiger Woods scraped into the weekend with nothing to spare as late errors from various afternoon starters pushed the cut line back to one under.
Simpson, the 2012 US Open champion, had started the tournament by compiling an accomplished 66 but accelerated clear of the field with a stunning spurt on the back nine on Friday. The rest, surely, are playing the tournament within the tournament. That was a month before he was sidelined with three more back surgeries. Actions will always speak louder than the upbeat words consistently offered by Woods.
The three-time major victor knows a little something about mounting a Sunday charge from the lower reaches of the leaderboard. The scale of reaction as Woods was in the middle of his charge only served to highlight once again what impact he has on a sport that not so long ago looked like it may have to resign itself to life without him.
He bogeyed 14 and then made par on the final four holes to close out the day.
Fellow Raleigh native Chesson Hadley entered play Saturday at 9-under but finished with a 2-over 74 Saturday and sits at 7-under heading to Sunday.
It was also the lowest score in Woods' 66 career trips around the Stadium course, where he won in 2001 and 2013.
Woods carded two birdies and one bogey in a second round of 71 to finish one under and ensure he would be around for the weekend. "I didn't have much of what I wanted. I felt I had better control of hitting it right-to-left and left-to-right, and consequently today I was able to shape the golf ball both ways and started to control it a little bit better today". I actually drove the ball unbelievably well the first two days and I hit my driver really poorly today and shot seven under.
He started out with an 8-foot birdie putt on the opening hole.
I had questions going into Saturday after Simpson built his lead mostly with his putter and short game. Before cooling off at the end of the round, he flirted with what would have been a course record, and he told reporters he considered 10-under on the day as a possibility.
Conditions were ideal for scoring for the second straight day.
Former Players Championship victor Phil Mickelson, who played alongside Woods for two rounds, added a 73 to his horror first-round 79 and at eight-over was headed home early. "I don't know, where is he at?"