Furyk - joint leader overnight - carded a five-under-par 65 to take control at 15 under overall after the third round at the Royal Montreal Golf Course in Quebec.
The American and 2003 US Open champion had his second consecutive bogey-free round, sinking five birdies, including back-to-back at the third and fourth holes.
Furyk - without a PGA Tour win since claiming The Tour Championship in 2010 - is well placed to end a wait of almost four years without victory.
Hot on his heels is South African Tim Clark, who is in sole possession of second spot at 12 under for the tournament.
Clark started the day in a tie for ninth but an eagle and four birdies saw him climb up the leaderboard with a blemish-free round of 64.
Two shots further back is American Kyle Stanley (68), who had three bogeys to go with his five birdies.
Counterpart Jamie Lovemark - six shots off the pace in fourth place - almost produced a bogey-free round but he dropped a shot at the 18th to him card a 67.
American pair Joe Durant (67) and Scott Brown (69) are both at eight under.
They are joined by Canadian hope Graham DeLaet (70), who slipped down the standings having started the round two strokes back.
Overnight co-leader Tim Petrovic (72) is also seven shots in arrears alongside the trio.
Gonzalo Fdez-Castano (69), Michael Putnam (69), Graeme McDowell (70) and Justin Hicks (70) are a shot further back.
Meanwhile, defending champion Brant Snedeker hit a 67 to close the day at five under - 10 shots behind Furyk.