His 11-under 131 total left him a shot ahead of Tyrrell Hatton, who also shot 63, and first round pacesetter Justin Rose (67 with a third Englishman, Tommy Fleetwood (65), two shots further back in fourth place.
Double 2018 major winner Brooks Koepka (69) and fellow Americans Tiger Woods (66) and Bryson DeChambeau (68) were all seven strokes off the lead with Northern Irishman Rory McIlroy (67).
DeChambeau, winner of last week's Northern Trust in New Jersey, led the FedExCup standings heading into the second of four playoff events on the PGA Tour.
Simpson, winner of the prestigious Players Championship in May, did not put a foot wrong on Saturday, carding six birdies as well as the eagle. He has just one blemish on his card through 36 holes.
Hatton did something almost unheard of on the PGA Tour last Saturday when he purchased a putter with his own money from a golf shop in New Jersey and it is looking like $172 well spent.
"I had to get a new putter," he said. "I was fed up with how the other one was working, or wasn't working. Hopefully the honeymoon period continues."
It was not only his putter that was working on Saturday, however.
"Anytime you shoot eight-under is a good day," said the three-times winner on the European Tour.
"Gave myself a lot of chances, irons were really good and it was nice to be in the fairway a little more today."
Hatton and Rose will be team mates for Europe against the United States at the Ryder Cup in Paris later this month, but rivals over the final two rounds this week.
For the second time in three events, Rose did not have a practice round. The exception was last week, where he ended up missing the cut.
The less is more approach seems to be working this week.
"I really enjoyed that way of preparing," said the 2013 U.S. Open champion. "I feel having not played I've almost been more keen and more interested and switched on.
"I've read the greens much better this week than last week and I guess that's reflected in my scoring."
(Reporting by Andrew Both; Editing by Ken Ferris/Nick Mulvenney)
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