Tiger Woods and Phil Mickelson were projected to miss the cut in West Virginia.
Simpson followed up his opening five-under-par 65 with a bogey-free 66, and led the way by one shot on nine under when play was suspended due to darkness with 12 players still on the course.
Rookie Charlie Beljan had five birdies in his first seven holes en route to a career-best eight-under 62 and a share of second place along with Jerry Kelly (66), Jeff Maggert (68) and Jonathan Byrd (68), with Martin Flores also on the eight-under mark with two holes to play.
JB Holmes (68) and South Korea's Charlie Wi (66) were a further stroke back in a tie for seventh.
Woods, meanwhile, finished level par after carding a 69 and Mickelson's second straight round of 71 left him two over. The projected cut was one under.
Watch: Simpson Leads Greenbrier.. More Videos
Overnight leader Vijay Singh slipped off the pace after following up his first-round 63 with a disappointing 74.
Woods headed into this event buoyed by victory in the AT&T National at Congressional last weekend - his third win of the season and fourth in seven months - and seeking back-to-back top-10 PGA Tour finishes for the first time since the start of 2010.
But he did not get into his groove on Friday and will not be around for the weekend despite picking up three birdies over his final seven holes.
"I didn't quite have it," the 14-time major winner said. "I just did not have the feel for the distances.
"The ball was just going forever. I didn't hit the ball pin high, and that's one of the hallmarks of my game. I can hit pin high pretty consistently and I just did not do that at all."
It marked the first time Woods and Mickelson had missed the cut in the same tournament as professionals.
"It happens," Woods added. "We miss cuts out here."