The 26-year-old from North Carolina moved to 14 under thanks to his second consecutive bogey-free round in West Virginia.
Simpson, who led by one stroke heading into the third round, started the day with six pars before collecting a birdie on seven – for the third time this week – and then gaining momentum on the back nine to extend his advantage.
Troy Kelly fired a blistering 62 to claim second spot, with Ken Duke (65), JB Holmes (66) and rookie Charlie Beljan (67) a further shot back on 11 under.
Despite his enviable position after three rounds, Simpson will not rest on his laurels on Sunday.
“The way I look at it is, I’ve got to go shoot under par [on Sunday],” he said on www.pgatour.com.
“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.
“I’ve almost got to imagine that these guys are all going to shoot four, five under. I’ve got to stay aggressive.”
Tiger Woods will not be around to trouble the leader after missing the cut for only the ninth time in his PGA Tour career.
“When he’s not lurking around on Saturdays and Sundays, it makes it a little easier I think for other guys,” Simpson added.