Dufner, who teed off with a two-shot lead, avoided most of the trouble with four early pars and, by doing so, expanded his lead to three shots, getting a chance to firmly establish control early in the round.
Instead, he pulled his drive on the par-four 5th into Allen’s Creek, leading to a double bogey and bringing the rest of the field closer.
Dufner appeared to recover from his slip on 5 with a birdie on 7, but missed a short par putt on 8, and dropped into a tie with Furyk, who shook off two early bogeys with birdies on 4 and 8 to turn in 35, catching Dufner and passing both Stenson and Adam Scott.
Then Furyk made an impressive birdie on the par-four 10th, pushing him into the outright lead for the first time since the opening round - but only until Dufner birdied 10 to climb back to eight under and tie things up again.
Furyk rolled in a 20-foot birdie putt on 12, and was back in the lead at nine under, chased by both Dufner and Stenson, the Swede enjoying three consecutive top-three finishes going into the week, including a runner-up to Mickelson at Muirfield.
Stenson was, perhaps, the steadiest player among the leaders, with just one birdie and one bogey in his first 12 holes to hang close before he birdied 13 and 14 to move to eight under, just behind Furyk.
Just as quickly, though, Stenson bogeyed 15, but he managed to par the last three holes and finished with a 69 to finish at 203, seven under par, giving himself a terrific chance to become the first Swedish-born player to win a major.
Furyk made with his own bogey at 15 to fall back into a tie with Dufner, but that deadlock would not last.