Furyk, who fired just the sixth 59 in PGA Tour history Friday, ended 54 holes at 13-under-par 200.
That was one better than the onrushing Steve Stricker, who zoomed up the leaderboard with a 7-under 64 to grab sole possession of second place at 12-under.
Second-round co-leader Brandt Snedeker notched an even-par 71, good for third at 11-under 202.
Zach Johnson carded a 2-under 69 to end the day in fourth at 10-under 203.
Five-time winner Tiger Woods finished Saturday alone in fifth at 9-under after a round of a 5-under 66, in which he carded birdies on six of the final seven holes.