Rose, who has produced stellar form this year since tying for second at the Masters in April, charged to the top with a sizzling seven-under 63 in slightly more receptive conditions at Firestone Country Club.
The world number eight birdied four of the last six holes in a bogey-free display to finish at nine-under 201, level with American Furyk who did well to sink a par putt from 11 feet on the final green for a 69.
"I haven't seen a putt go in all week from outside eight feet, it feels like," Rose told reporters after he celebrated his monster putt on the 18th green with a wink to the crowd.
"To knock that ball in on the last, it was a nice bonus for sure. My game's in good shape. If I look back at Augusta, that was the start of me feeling very confident."
Rose, who won his seventh PGA Tour title in New Orleans in April, has recorded five top-10s on the U.S. circuit this season, including a playoff loss at the Memorial Tournament in June and a tie for sixth at last month's British Open.
"If I keep knocking on that door, I feel good," said the 35-year-old Englishman. "The only tournament I feel like I've let slip this year is Memorial."
Ireland's Shane Lowry, seeking his first victory on the PGA Tour, was alone in third place at seven-under after carding a five-birdie 67 at the elite World Golf Championships event.
Australian Steve Bowditch, who matched Rose with the lowest score of the week, was a further two strokes back with England’s Ian Poulter (65), Swede Henrik Stenson (68) and American Bubba Watson (69).
Masters and U.S. Open champion Jordan Spieth, who had been six strokes off the pace overnight, tumbled down the leaderboard as he struggled to a two-over 72 that included a double-bogey at the last.
"Very frustrating today," said the American, the biggest drawcard this week in the absence of world number one Rory McIlroy, who was recovering from an ankle injury, and eight-times former champion Tiger Woods.
"It was a poor performance. Didn't have very good control of the ball. I putted it OK, but other than that, very much struggled.
"I'm going to need to look for some answers tomorrow and into next week," said Spieth, referring to the year's final major, the PGA Championship at Whistling Straits.
(Reporting by Mark Lamport-Stokes in Akron, Ohio; Editing by Larry Fine)
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