Clark closed with a 5-under 65 at rainy Royal Montreal for his second PGA Tour victory. The 38-year-old South African player also won the 2010 Players Championship.
Furyk, the two-time Canadian Open champion who took a three-stroke lead into the final round, finished with a 69. The 44-year-old American matched Clark with a birdie on the par-3 17th and a par on the par-4 18th.
"It looked like Jim wasn't going to make any mistakes," said Clark, who moved into contention Saturday with a 64. "He was pretty solid, so I knew I had to make birdies. At that point, there was nothing to lose. Suddenly I got hot and I went with it."
Furyk is 0 for 7 with the 54-hole lead since winning the 2010 Tour Championship for the last of his 16 PGA Tour titles
"I kind of controlled my own destiny," Furyk said. "I've got to shoot 3 or 4 under and it would have been impossible to catch me, or darn near it. I left the door open with even par on the front nine and Tim took advantage and shot 30 on the back."
On No. 18, Clark left a 45-foot birdie putt about 6 feet short, and Furyk missed left on a 12-footer. Clark sealed the win by holing the 6-footer for par.
"Once he missed his putt, I didn't want to have to go into a playoff, knowing he can take it over the water (off the 18th tee) and I have to play over to the right," Clark said. "So, it was huge for me to get it finished right there. I got hot with the putter on the back nine. To stand over that putt and still feel confident was really nice."
Clark, four strokes behind Furyk after bogeying the par-4 first, took the outright lead with a birdie on the par-4 16th after a short rain delay. Clark finished at 17-under 263 to tie tournament record for total score set by Johnny Palmer in 1952 at St. Charles in Winnipeg, Manitoba, and matched by Scott Piercy in 2012 at Hamilton in Ancaster, Ontario.
Clark's wife, Candice, is from Toronto and has family in Montreal. He won his first pro title at the New Brunswick Open on the Canadian Tour in 1998 and followed a week later with a win at the CPGA Championship.
"The irony of it is Canada could be the location of my first win and my last one," Clark said. "To come back here, it's full circle. That was 16 years ago when I was just cutting my teeth as a professional golfer and I was fortunate enough to be given some starts up here, so I have fond memories.
"It's certainly one I've wanted to win for a long time. Any national championship to me is special. particularly to the people from that country. It's an honor for me to be the open champion."
Graham DeLaet, from Weyburn, Saskatchewan, was the top Canadian, closing with a 68 to tie for seventh at 10 under. Pat Fletcher, born in England, was the last Canadian winner, taking the 1954 event at Point Grey in Vancouver.
"I fell a little short, but it was fun," DeLaet said. "So many people were cheering for me. ... Coming down 18 was a special moment.
Dicky Pride also finished at 10 under, matching the course record with a 63.
Organizers moved up the starting times by two hours and had the players went out in threesomes from both the first and 10th tees to try to finish before the forecast storms. Most of the players had finished before a cloudburst halted play for 26 minutes.