Simpson, who won the US Open in 2012 in San Francisco, made four birdies on a bogey-free back nine, while Armour birdied four straight holes en route to a nine-under par 61.
The pair were tied at 13-under 127 for a one-shot lead over Sweden’s Henrik Stenson, who led the morning groups with a four-under 66 at Sedgefield Country Club in Greensboro, North Carolina.
“We’re obviously close to where I grew up,” said Simpson, who comes from North Carolina. “I grew up playing courses similar to this that aren’t too long, hit different clubs off the tee, some doglegs.
“There’s a comfort here that I feel like I don’t have at a lot of places. I’ve always loved playing close to home. That’s part of it as well.”
Simpson, who won his first PGA Tour event in North Carolina in 2011, had to overcome back-to-back bogeys on the front nine, while Armour drained a total of nine birdies.
Vaughn Taylor (66) and Ollie Schniederjans (63), who birdied three of his last four holes, were tied for fourth at 11 under.
Hunter Mahan (65) Kevin Na (63) and former winner Davis Love (66) are next at 10 under. Mahan had his second consecutive 65.
Stenson, the highest-ranked golfer in the field at ninth in the world, carded birdies on three of four holes during one stretch as he finished on the front side.
“I felt like I was fighting the feeling a little bit about the swing,” Stenson said. “I still managed to produce some good stuff. I managed to scramble and keep it tidy anyway.”
One of the most entertaining rounds of Friday belonged to Johnson Wagner, who shot 64 despite ending with a bogey. He is nine-under for the tournament in a group of five golfers that also includes Ireland’s Shane Lowry (64) and American Harold Varner (68).
Wagner posted an albatross — a double eagle on the par-five fifth hole after holing out his second shot, marking the second one of his US PGA Tour career. Ten holes later, he posted an eagle.
First-round leader Matt Every shot a two-over 72 and was tied for 19th.
This is the last tournament of the regular season before the FedEx Cup playoffs, so golfers such as Varner and Mahan need good finishes to qualify for the playoff events.
“I was able to feel really confident and free out there and was aggressive with a lot of iron shots,” said Mahan, who is seeking his seventh US PGA Tour win. “Felt great to be out there just playing well and not stressing about every single shot.”