Simpson could not replicate his fine form in the opening couple of days, which had seen him reach 15 under par overall at TPC Summerlin after rounds of 64 and 63.
But his four under par on Saturday was enough to keep him four shots clear of his closest challenger, and it would appear only something spectacular will keep him from winning his first tournament since the 2012 US Open.
The 28-year-old bounced back from making a bogey at the par four third with successive birdies at his next two holes although he dropped another shot to leave him level par for the round after 11 holes.
Once again, though, the American responded to a bogey by picking up shots on his next two holes before further birdies on the 15th and 16th helped him to a strong finish.
Chesson Hadley is in second after matching his compatriot's third-round score to reach 15 under par overall.
Hadley made a terrible start with a double bogey at the third, but that was to prove his only blemish of the afternoon.
He holed his approach shot from 98 yards to eagle the par-five 16th to at least ensure Simpson did not strengthen his overnight position.
Jeff Overton, who is yet to win on the PGA Tour, will go into the final round trailing Simpson by five shots following a bogey-free 68, which takes him to 14 under par overall.
The 30-year-old made a bright start with a birdie on his opening hole and added to that by picking up shots at the fourth and 16th.
Jason Bohn is a shot further back after his two under par round. The American looked on course for a stunning day after opening with three birdies in his first four holes, but he double bogeyed the sixth and his challenge did not recover.
First round leader JJ Henry is among six players in a tie for fifth.
Henry broke the course record on Thursday after shooting 60 but rounds of 71 and 70 has seen his challenge stagnate.
He lies alongside fellow Americans Sean O'Hair - whose eight under par was the round of the day - William McGirt, Ryan Moore and J.J. Henry, and Scotland's Russell Knox on 12 under par.