The American followed up his opening day 64 by going one stroke better on day two to move to 15 under par overall at TPC Summerlin.
Starting on the back nine, the 2012 US Open champion made three birdies in his first five holes before his only blemish of the day with a bogey at the par-five 16th.
He responded with back-to-back birdies directly before and after the turn, and added to that by picking up shots on the fourth, fifth and six holes as he finished the day four shots clear of five players.
"I hit a couple of loose shots but I managed to make putts and take advantage of the holes that you have to make birdie on," Simpson told the PGA Tour website.
"We stayed away from the trouble and I'm just thankful to shoot another good one.
"I haven't won this year, but my one goal every year is to get better, and I felt like I got better."
Overnight leader JJ Henry was one of the players in a tie for second after falling some way short of following up a superb, course-record 60 on the opening day.
The American recorded nine birdies and one eagle in an unblemished first round, but he opened his account on day two with three bogeys in his first four holes.
Although he recovered with three birdies, he dropped a shot at the last to card a level-par 71 to sit alongside fellow Americans Jeff Overton, Chesson Hadley and Jason Bohn, and Australian John Senden.
Bohn was one of the biggest movers of the day and looked to be closing in on Simpson after nine birdies in 16 holes took him to 16 under overall.
But a double bogey on the par three 17th dropped him back amongst the chasing pack.
American Ryan Moore and Scotland's Russell Knox are on 10 under overall to sit in a tie for seventh, while Luke Guthrie, Stephen Ames, Ryo Ishikawa and Brian Stuard are a further shot back.