"I wasn't swinging my drivers as well as I did yesterday, and that made it hard to adjust the distance of my iron shots".
But the 41-year-old sank nine birdies - five of which came on the opening nine holes - to soar up the leaderboard and beat his previous best round by two shots.
"I'm very hungry to win again but right now I got dinner on my mind", said Simpson, a four-time tour victor, including the 2012 U.S. Open.
Stenson's run of four birdies in five holes down the back stretch saw him pull level with Simpson in the lead before the latter bogeyed the 17th to drop back.
Simpson, the 2011 champion, carded 64 on Friday while Armour went even lower with a career-best nine-birdie, nine-under-par 61 in ideal if sweltering conditions.
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But the day belonged to Armour, who recorded nine birdies - including four in a row from the fifth to the eigth - on his blemish-free scorecard.
At 125th on the FedEx Cup points list, he lived to fight on at the weekend, with a great chance of finishing on Sunday among the top 125 in the standings to be fully exempt for next season. "I had some goals at the beginning of the week".
"With a 31 on the front nine I put myself in good position to shoot a good score but I had a couple of unforced errors on the back", he said.
They led by one stroke from Swede Henrik Stenson, who eschewed a driver for the second straight day while carding 66. "I got to keep the hammer down". This is the last event before the playoffs start, so all the bubble players will be fighting their own battles Sunday at Sedgefield Country Club.
Davis Love III is part of a group of players at 13-under following a third round of three-under 67 while Europeans Soren Kjeldsen and Shane Lowry both finished Saturday at 12-under following rounds of 66 and 67.
"I hit a lot of good shots out there", Stenson told Sky Sports.