While seven-times winner Tiger Woods also made a strong start, firing a four-under-par 66, Simpson seized control of the elite World Golf Championships event with an eight-birdie 64.
On a breezy day of sunshine and sporadic cloud cover at Firestone Country Club, former US Open champion Simpson was in sizzling form on the greens, totalling only 22 putts to end the round a stroke in front of Swede Henrik Stenson.
Woods, who has triumphed a season-high four times on the 2013 US Tour, mixed six birdies with two bogeys to sit a further shot back, level with fellow Americans Ryan Moore and defending champion Keegan Bradley, and Englishman Chris Wood.
Former world number one Luke Donald of England bogeyed his final hole, the par-four 18th, to card a 67 and end the round alongside Americans Bubba Watson, Jason Dufner, Rickie Fowler, Bill Haas and Jim Furyk.
Simpson was elated to be the tournament's front-runner after taking full advantage of advice from his experienced caddie on how to play the heavily tree-lined Firestone layout.
"It was a great start," the 27-year-old American said after setting the tone for a low round on a rain-softened layout with four birdies in his first nine holes.
"My caddie has been here so many years and I had to listen to him. He basically showed me where to go yesterday and told me where to hit it, where the lines were, what clubs to hit.
"Today was one of those days where I just saw the lines well, and my speed was really good. You've got to have great speed because there's so much slope in the greens.
"And the better the speed, the bigger the hole," said Simpson, who missed out on making his debut at Firestone last year due to the birth of his daughter Willow.
Simpson has not triumphed on the US Tour since he clinched his maiden Major victory at the 2012 US Open but he has been happy with his improving form on the circuit this season.
"It's encouraging and frustrating because I haven't won and yet I'm 17th in FedExCup (standings)," he said. "I feel like I've let a couple of tournaments go that maybe I should have closed out or at least I should have contended more."
Simpson has recorded four top-10s in 18 starts on the 2013 US Tour, his best finish a play-off loss to Northern Ireland's Graeme McDowell at the RBC Heritage in April.
"If I'm getting better, I'm happy," said Simpson. "And I do feel like I'm getting better, I just don't have the results this year to show it."
Woods has certainly had the results with four US Tour wins this season and he swiftly moved into familiar territory at Firestone, covering his back nine in four-under 31 to rocket up the leaderboard.
"I felt pretty good today," said the 14-times Major champion. "I feel very good about what I'm doing with basically my whole swing. I hit a lot of good shots. I had a really good feel for the distance today. I thought I putted well."
Woods has won a record seven times at Firestone, and has piled up a staggering 11 top-10 finishes in 13 appearances at the elite event.
"For some reason this golf course, I just see it," said the world number one. "It's just one of those venues. Luckily over the years I've taken advantage of it. I have played well and I've scored well, and I've won my share of tournaments here."
Northern Irish world number three Rory McIlroy returned a roller-coaster 70 while newly crowned Open champion Phil Mickelson opened with a 72 to sit joint 41st in the 73-man field.
"Some good, some bad," McIlroy said after carding five birdies, three bogeys and a double at the par-four 10th. "I felt like I hit a lot of good shots out there.
"I drove the ball well for the most part, gave myself a lot of chances for birdies, and I just threw a few shots away around the greens, made double at 10 from nowhere. Felt more comfortable with my putting, which was a good sign."
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- Tiger Woods
- Firestone Country Club