WHITE SULPHUR SPRINGS, West Virginia, July 7, 2012 (AFP) - Simpson posted a five-under par 65 that included five birdies and no bogeys for a 54-hole total of 14-under par 196.
That put him two strokes in front of Troy Kelly, who had eight birdies in an impressive eight-under 62 on the Old White TPC course for a 12-under total of 198.
It was a further stroke back to Ken Duke (65), Charlie Beljan (67) and JB Holmes (66) on 199.
Simpson, who claimed his first major title with his US Open triumph at The Olympic Club in San Francisco last month, has played 48 straight holes without a bogey -- his last miscue coming at his sixth hole of the first round.
He birdied four of his last six holes on Saturday to gain a bit of breathing room atop the leaderboard, but 20 players were within six shots of his lead.
Although the bunched field promised an unpredictable Sunday, two players Simpson won't have to worry about are Tiger Woods and Phil Mickelson. Both missed the cut on Friday.
It was Woods's second missed cut of the season but just the ninth of his pro career. Simpson said he was not sorry that the 14-time major champion wasn't going to be around.
"When he's not lurking around on Saturdays and Sundays, it makes it a little easier, I think, for other guys," Simpson said.
Simpson said he fully expects someone to come out of the pack and challenge him on Sunday.
"The way I look at it is, I've got to go shoot under par. And if I don't, somebody's probably going to (play) pretty good. I think the golf course is playing in such a way that there's plenty of birdie opportunities."
Simpson briefly led this tournament going into the back nine of the final round last year. He faded to finish equal ninth.
"I realized shortly after the round that I wanted it so bad that it kind of put more pressure on myself than the pressure I was already feeling," he said. "So it kind of locked me up a little bit and I wasn't able to perform like I had been all week."
It's a lesson he's tried to remember, and since that disappointment he's gone from strength to strength.
On Saturday he stayed patient with six straight pars before nabbing his first birdie of the day at the seventh.
He regained the lead from Kelly with his fourth birdie of the day at 17, where he drained a six-foot putt, and then rolled in a 20-foot birdie putt at the par-three finishing hole.
Among his pursuers, both Kelly and Holmes are coming back from medical battles.
Kelly had hip-replacement surgery in September 2010 after being diagnosed with arthritis.
Holmes had brain surgery in September 2011 after vertigo symptoms led to a diagnosis of Chiari malformations -- a structural defect in the part of the brain that controls balance. He returned to the tour in January.
Leading third-round scores on Saturday in the $6.1 million US PGA Greenbrier Classic (USA unless noted, par 70):
196 - Webb Simpson 65-66-65
198 - Troy Kelly 69-67-62
199 - Ken Duke 66-68-65, J.B. Holmes 65-68-66, Charlie Beljan 70-62-67
200 - Ted Potter jnr 69-67-64
201 - Blake Adams 67-70-64, Graham DeLaet (CAN) 67-70-64, Charlie Wi (KOR) 67-66-68, Martin Flores 64-68-69
202 - Bill Haas 68-69-65, Keegan Bradley 68-68-66, Carl Pettersson (SWE) 71-65-66, Seung-Yul Noh (KOR) 68-67-67, Jeff Overton 70-65-67, Steve Wheatcroft 70-68-64, Scott Piercy 66-68-68, Billy Mayfair 69-65-68, Bob Estes 69-65-68, Jerry Kelly 66-66-70, Jonathan Byrd 64-68-70
203 - Billy Horschel 66-70-67, Daniel Summerhays 68-67-68, Davis Love 69-66-68, Sean O'Hair 66-68-69
204 - Johnson Wagner 68-69-67, Patrick Cantlay 67-70-67, Steve Stricker 69-67-68, Kevin Na 69-67-68, David Hearn (CAN) 69-68-67, Justin Thomas 67-71-66, Kevin Chappell 69-66-69