It was the third straight round of four under par by Slocum, whose 12-under-par 198 total was a shot better than compatriots Joe Durant (68) and Troy Merritt (64).
"Just another solid day," the 36-year-old Slocum told reporters. "Drove it well again, only missed a couple fairways. Hit some good iron shots. Minimized the mistakes. Made some putts.
"That's kind of I would say the formula to get around this place. I think that's what I've done for three straight days."
A further stroke back was second-round leader David Toms, who offset two birdies with a pair of bogeys en route to an even-par 70 for 200.
Slocum birdied three of four holes from the fourth and added birdies at the 11th and 14th before dropping a shot at the par-four 16th when the wind suddenly died and his approach flew over the green.
It was Slocum's first bogey since the opening hole of his first round when he dropped a shot on the par-four 10th.
Australians John Senden (67) and Aron Price (66) were among a group of players tied on 201, with compatriots Robert Allenby (66) and James Nitties (68) another shot back along with Arjun Atwal of India (67).
Slocum, who has four top 10s this season, claimed his third U.S. PGA Tour victory at last year's Barclays, the opening event of the FedExCup playoffs, which he said had given him a confidence boost.
"I just confirmed at the Barclays what I always felt like -- I could compete with the best for sure, in any given week."
(Reporting by Larry Fine in New York; Editing by Frank Pingue)