Furyk drained birdie putts on each of the final two holes to hang onto the lead at 9-under-par 201, holding off Jason Dufner on the East Course at Oak Hill.
Dufner turned in a round of 1-over 71 to grab sole possession of second place at minus-8.
Henrik Stenson, who along with Furyk has carded three rounds in the 60s this week, fired a 1-under 69 to finish 54 holes at 7-under-par 203, good for third place.
Swedish countryman Jonas Blixt, meanwhile, finished Saturday alone in fourth at 6-under 204 following a third-round 4-under 66.
Four-time PGA Champion Tiger Woods struggled to a 3-over 73, finishing 54 holes at plus-4.