The local favorite moved to 15-under 195 for the tournament, and was well positioned for his first PGA Tour win.
The 26-year-old North Carolina native had four birdies and an eagle during his late charge at the final event before the playoffs start next week.
"You've got to really stay patient around this golf course, because bogeys are pretty quick to happen out here with the rough and the undulating greens," Simpson said. "I told myself to be patient and let the birdies come. It took them a while to get there, but finally made a few coming in."
Tommy Gainey (69), who led or shared the lead after each of the first two rounds, was 13 under.
Carl Pettersson (63) and John Mallinger (65) were 12 under. Daniel Summerhays (68) was 11 under, and Billy Horschel (66), Charles Howell III (66), Jason Bohn (67), Retief Goosen (68) and Ernie Els (69) were another stroke back.
Play was halted for 1 hour, 4 minutes late in the day due to threats of rain and lightning.
After things resumed, Simpson made his move.
He started the day three strokes behind Gainey and had two early bogeys before leapfrogging his playing partner with a barrage of low scores.
Simpson birdied No. 13 and sank a 32-foot birdie putt on No. 14. He stuck his second shot on the par-5 15th within 5 feet of the flagstick and converted that putt for his third eagle of the week. He had consecutive birdies on Nos. 16 and 17, then nearly closed his round with another - but left his 18-foot putt 2 inches short.
"Probably one of my top birdie-eagle streaks that I've had, and it came at a better time than any other streak I've had, just because we're not getting anything going all day and everybody else is taking it low," Simpson said. "To finish the round that way was great. I'd much rather finish the round that way than start that way. If at all possible, we'll start that way (Sunday)."
Gainey, a South Carolina native nicknamed "Tommy Two Gloves," built his two-round lead after having just one bogey on Thursday and Friday, but he doubled that total on his first two holes Saturday, and that opened things up for the rest of the field.
"I guess one word sums it up - frustrating," Gainey said. "That's the only positive thing that I can take from it right now, is I still have a chance to win the golf tournament. That's all you can ask for, teeing it up Round 1 to Round 4."
Pettersson was the first to take advantage. He began the day seven strokes back, but had an eagle on the par-5 No. 5 to go with five birdies, including one on the par-3 16th that put him in front at 12 under.
Now he'll enter the final round in contention for a second victory on his adopted hometown course.
The native Swede grew up locally, played college golf at North Carolina State, serves on this tournament's board of directors and won it in 2008. He's making the daily 112-kilometer (70-mile) commute from his home in Raleigh.
"The golf course is finally tougher than in years past," Pettersson said. "It's nice to put myself back in the tournament, and I don't know what's going to happen. Today I've done my bit and I probably (have) got to go a low (score) tomorrow again."
Mallinger, who began the day five shots back, followed a bogey with three straight birdies on Nos. 15-17 to vault into the lead at 13 under. His tee shot on No. 18 sailed into the woods and he caught a fortunate bounce when it kicked back into play, but his 27-foot par putt trickled past the hole and he tapped in for bogey.
The 31-year-old, chasing his first PGA Tour victory, is playing just his 14th tournament this season. He made it to the weekend for just the sixth time this year. He tied for third here last year.
"The greens (at Sedgefield) are the same greens I practice on at home," Mallinger said. "So that's a big thing for me, just being comfortable on every tee box."
Webb Simpson leads by 2 shots after round 3 at Wyndham
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