Furyk, who was in a three-way tie for second with Adam Scott and Matt Kuchar when the round began, offset two early bogeys with a pair of birdies on the front nine and then grabbed the outright lead with a birdie on the par-four 10th.
Dufner, who began the day two shots clear of the pack but was forced to settle for a slightly disappointing one over par 71 after his course record 63 on Friday, was cruising along with a string of pars and leading by three when his tee shot at the par-four fifth went into a creek well right of the fairway.
After sending his third shot right of the green and chipping well past the hole, Dufner two-putted for a double-bogey six that cut his lead to one stroke.
The 33-year-old recovered nicely with a par before curling in a 10-footer for birdie at the par-four seventh that re-established his two-shot lead.
But Dufner went bogey-par over the next two holes to reach the turn in two-over 37 as sunny skies and blustery conditions combined to make the greens quicker and low scoring at a premium.
Furyk continued to prosper on the back nine as birdies on 10, 12, 17 and a brilliant par save on 18 from off the green helped him move from seven under to lead on nine under.
His round of 68 contained five birdies and three bogeys, and justified his standing as the new tournament favourite a decade after he won his only Major at the 2003 US Open.
"I made a bad swing at 18, but went wedge, wedge and holed a 15 footer. It was an exciting way to end the day," said Furyk.
"Any time you are in contention for a Major championship, it is exciting..I always think you try to learn from your mistakes, and I hope my experience can help me tomorrow."
Dufner added: "A lot of things can happen out there tomorrow. You have to be patient, and hope some of the breaks go your way."
Swedes Henrik Stenson and Jonas Blixt are also well in the hunt for their first Majors. Stenson made 69 to finish on minus seven with Blixt a stroke further back after a 66 left him on minus six.
Blixt did not make a bogey in his round.
No one in the final five groups in the third round of the year's final major was able to shoot under par through their opening nine holes on Saturday.
Masters champion Scott got off to a quick start by draining a 20-foot birdie putt at the first to move one shot behind playing partner Dufner but he handed it back at the second with a bogey.
Scott fell three shots off the lead at the par-three third after finding a greenside bunker off the tee and then sending his par putt two feet past the hole.
But he made two commendable pars to keep himself in the hunt as he signed for a 72. He is at minus five.
Kuchar also got to within one shot of Dufner with a birdie putt at the opening hole after his approach from 186 yards landed about three feet from the pin.
But he had a double-bogey and three bogeys over his next eight holes to drop out of contention.
The game's two leading players, Tiger Woods and Phil Mickelson, both tumbled further out of contention, Woods battling to a 73 and Mickelson returning a 78.
Woods, who started the day 10 strokes off the pace, immediately fell further behind when he bogeyed the par-four first, missing the fairway to the left and failing to reach the green in regulation.
Woods, who has failed to break par in seven rounds of major championship play at Oak Hill, finished with four bogeys and a birdie and was never able to give himself many chances at making a run.
Mickelson, who captured his fifth major title at last month's British Open, was also unable to shoot himself into contention after starting the round 11 shots off the lead.
Mickelson, whose card included a triple-bogey, double-bogey, five bogeys and two birdies, bypassed the awaiting media after his round and left the course.
Defending champion Rory McIlroy, who was five over for the tournament at one point on Friday and in danger of missing the cut, roared back into contention with a three-under 67 that included four birdies and a bogey.
He capped his round in brilliant fashion, taming Oak Hill's infamous tough closing stretch with birdies at 17 and 18, including a chip-in from behind the green at the last.
"The way the conditions are with the swirling wind, it's tricky out there," said McIlroy.
"I felt good enough about my game that I could go out there and post a good one today and at least give myself a chance going into tomorrow."
AFTER THIRD ROUND
-9 J Furyk (US)
-8 J Dufner (US)
-7 H Stenson (Swe)
-6 J Blixt (Swe)
-5 S Stricker (US), A Scott (Aus)
-3 L Westwood (Eng), R McIlroy (NI)