Furyk fired a 7-under 63 in the opening round on Thursday, avoiding any bogeys and setting the scoring record in an early group at Hamilton Golf & Country Club.
The duo has a one-shot lead over three players.
'I heard coming up here how good the course was and I think it definitely met expectations,' said Furyk, who is playing in this event for the first time since 1999.
Furyk likes the feel of old, traditional courses and compares this week's venue to the courses he grew up playing in Pennsylvania.
'[Y]ou look at my schedule on TOUR, I tend to play the golf courses that fit that bill,' he said. 'And this is definitely that style. It's a very good one.'
Mixing his driver and 3-wood almost equally, Furyk hit 13 of 14 fairways in damp conditions and posted all of his red numbers on par fours and fives.
'I think there's a lot of options off the tee here,' Furyk said. 'You can kind of be more aggressive, you can do some different things. With it being softer, I think you're seeing some guys be more aggressive right now.'
Furyk has made just three cuts in five previous starts at the Canadian Open, with his best finish a tie for 22nd in 1998. But he's had a terrific season, posting one win and seven top-10 finishes in 11 starts since the Masters.
His eagle on Thursday came at the par-4 12th -- his third hole -- with an uphill 9-iron from 120 yards. From there, Furyk added birdies at the 15th and 17th to make the turn at 4 under.
He birdied back-to-back holes from the fourth, then finished off his 63 with a 6-foot birdie putt at the ninth to take a one-shot lead at the time.
Afterward, Furyk raved about the par-70 layout.
'[W]e had a couple of the guys in our scoring tent, the officials that we have that take our score cards and they said they'd never seen so many guys come in and shoot 75 and rave about a golf course,' he said.
'I shot a low number, but I was obviously aided by the weather and the conditions of the golf course. We were fortunate that it was soft.'
Rose, who owns just three top-10 finishes in 22 starts this season, didn't par a hole until the sixth. He opened with four birdies and a bogey over his first five holes, then added birdies at seven and nine to make the turn at 5 under.
Another birdie at 14 and a tap-in birdie at the par-5 17th tied him with Furyk.
'I feel like I'm playing a little better,' said Rose, who tied for fourth at the Deutsche Bank on Monday. 'I'm thinking a little better and I'm putting a little better.'
Brandt Jobe, Frank Lickliter II and Nathan Green each shot 6-under 64 to share third place.
Reigning Rookie of the Year Sean O'Hair birdied his last three holes to lead a group of five players who are tied for sixth place at 5-under 65. He was joined by Jesper Parnevik, Arron Oberholser, Jonathan Byrd and Bubba Watson.
Defending champion Mark Calcavecchia opened with a 66 and shares 11th place three others.
Mike Weir, the top-ranked Canadian in the world, is tied for 92nd place following a 71. Weir has a disappointing history in his national open, missing the cut in 10 of his 15 starts.
James Lepp, Darren Griff and David Hearn are the low Canadians at 1-under 69.