Clark, who won the prestigious Players Championship four seasons ago, posted a final round five-under par 65 on Royal Montreal's Blue Course for a 17-under total of 263 and a one-stroke victory over Furyk.
Furyk, 44, took a three-stroke lead into the final round and seemed poised to claim a third career Canadian Open title, and end his own victory drought stretching back to his 2010 Tour Championship triumph.
Like Clark, the American had just one bogey and one birdie on the front nine, but he couldn't find the birdies he needed to hold off the hard-charging South African coming in, signing for a one-under 69 for 264.
Even for the day through nine holes, Clark caught fire with back-to-back birdies at 11 and 12. He added another brace at 14 and 15 to move ahead of Furyk, who balanced a bogey at the fourth with a birdie at seven then made nine straight pars before matching Clark's birdie at the par-three 17th to head to the last one adrift.
Furyk was unable to convert a 12-foot birdie attempt at 18 to force a playoff as both players capped the round with pars at the 72nd hole.
Furyk, coming off a fourth-place finish at the British Open at Hoylake last week, has now failed to convert his last seven 54-hole leads to victories.
Leading final-round scores on Sunday in the PGA Tour $5.7 million Canadian Open (USA unless noted, par-70):
263 - Tim Clark (RSA) 67-67-64-65
264 - Jim Furyk 67-63-65-69
267 - Justin Hicks 66-67-70-64
269 - Matt Kuchar 69-65-70-65, Michael Putnam 64-70-69-66, Gonzalo Fernandez-Castano (ESP) 67-67-69-66
270 - Dicky Pride 66-71-70-63, Graham DeLaet (CAN) 69-63-70-68
271 - Kevin Kisner 70-69-68-64, Brad Fritsch (CAN) 72-68-67-64, Graeme McDowell (NIR) 68-65-70-68
272 - Ben Curtis 67-70-70-65, Ernie Els (RSA) 70-67-69-66, Nick Watney 66-68-71-67, Troy Matteson 70-68-67-67, Retief Goosen (RSA) 69-67-69-67, Jamie Lovemark 69-65-67-71, Joe Durant 69-66-67-70, Kyle Stanley 65-67-68-72
273 - Robert Allenby (AUS) 66-69-72-66, Kevin Chappell 72-67-68-66, Andres Romero (ARG) 71-68-67-67, Matt Bettencourt 67-70-68-68, Scott Brown 67-66-69-71
274 - William McGirt 69-70-69-66, Scott Piercy 72-65-71-66, Will Wilcox 68-68-69-69, Brandt Snedeker 69-69-67-69