Clark, who won the prestigious Players Championship in 2010 for his only prior PGA Tour title, 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 -- calmly sinking a 10-footer at 15 in the wake of a 25-minute rain delay.
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, his attempt sliding wide after Clark left a long birdie putt six feet short.
Clark made his par attempt to seal the win.
"I didn't really want to play 18 again in a playoff," said Clark. "It was huge for me to get it finished right there. I just got hot with the putter on that back nine."
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.
"I've got no one to blame but myself," said Furyk who didn't make a putt from outside four feet on the back nine.
"I played definitely good enough to win the golf tournament, but I only made two birdies and I've got to make more putts."
Clark's 17-under 263 total tied the 72-hole Canadian Open record set by Johnny Palmer in 1952 and Scott Piercy in 2012.
Graham DeLaet was the top Canadian with a tie for seventh. No Canadian golfer has won their home open since Pat Fletcher in 1954.