Furyk followed up Thursday's 63 with another strong performance, ending at 11-under 129 on the South Course at Firestone Country Club.
That's two better than Rafael Cabrera-Bello, who registered a 5-under 65 to end at 9-under 131.
Louis Oosthuizen carded a 65 to grab sole possession of third at 8-under.
Jason Dufner managed a 4-under 66 to go into the third round in fourth place at 7-under.
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