Walker fired a flawless eight-under 62 at the Sedgefield Country Club in North Carolina, to move to 12-under for the tournament ahead of US Open champion Simpson (63), who was also bogey free in the defence of his inaugural US PGA Tour win.
"I hit a lot of 5-woods off tees, kind of boring. I'm playing with J.B. (Holmes) and he's bombing the driver everywhere," Walker, looking for his first win on tour, said.
"I'm just kind of bunting the 5-wood around and hitting good approach shots, that kind of stuff. It was pretty boring looking golf.
Three-times tour winner Simpson was happy with his performance as he was cheered on loudly at his local event.
"I felt good kind of the whole game today," the 27-year-old said.
"Just one of those days where you really appreciate what you do just because its fun, go out there and play well, hit the ball where you're looking and start your putts on line and you can do that for a full day, it's always fun.
"I live an hour and a half away, I grew up an hour and a half way. Went to school 20 minutes from here. Good feeling when you hear people calling your name and rooting for you," the American added.
While the field is jostling for play-off seeds or positions in the top 125 for the FedEx Cup, Spain's Sergio Garcia is also fighting for a place in the European Ryder Cup team having been bumped from the automatic qualification zone by Briton Ian Poulter last week as the selection deadline looms.
Garcia showed he was not ready to give up on his aspirations of playing in a sixth European team as he fired a 63 to take a share of third place alongside South African Tim Clark (67), American Harris English (64) and overnight leader Carl Pettersson (68) of Sweden a shot further back at 130.
The Spanish world number 29 sunk seven birdies in a bogey-free round to give himself a great chance to move back into the mix.
"Everybody knows how much the Ryder Cup means to me," Garcia said.
"I have a chance this week. I'm going to give it my best shot. Hopefully my game will be on the weekend and I can get myself back in it. If not, then I'll have to hope for a pick.
"I love the Ryder Cup and I would love to be in it. If I'm in it, I'll give it my best and I'll try to bring as many things as I can to the European team. If I'm not I'll be the No. 1 fan watching at home on TV."
American Tim Herron produced a stunning turnaround from his six-over 76 first round, firing an course record-equalling 61 to make the weekend and keep his slim play-off hopes alive.
For others, though, the play-off dream is already over after missing the cut.
Double heart-transplant recipient Erik Compton (144) and former Major winners David Duval (143) and John Daly (140) will fall short after failing to make the weekend.
Gary Woodland, starting the week just outside the play-off mark, had a six-foot putt to make the cut and keep his chances alive when the horn blew to stop play.
But on his return after a delay of just over an hour, he missed the putt and with it a place at next week's Barclay's tournament.