New Zealand was up 19-0 at the half and went on to win on two tries from Sherwin Stowers and a try each from Kurt Baker, Pita Akhi and Gilles Kaka, who added three conversions.
Harry Jones and Nanyak Dala had tried for Canada. Team captain Nathan Hirayama converted Dala's try.
New Zealand, the dominant team in the annual world series but winner of its only World Cup 12 years ago, opened the scoring quickly. Baker scored a try 1:27 into the game, and Kaka's convert gave the Kiwis a 7-0 lead.
New Zealand went up 14-0 when Kaka converted Akhi's try at 3:42 of the first half. Stowers added an unconverted try less than two minutes later, and New Zealand went into halftime with a 19-0 lead.
Canada got on the board just 42 seconds after the break as Jones's try cut the lead to 19-5. But Stowers restored New Zealand's lead with his second try of the match at 2:21 of the half.
Dala's try and Hirayama's conversion narrowed the lead to 24-12 and gave Canada life, but with time running out Kaka converted his own try to put the game away for the favourites.
Every team made a single appearance before a sparse crowd at Moscow's Luzhniki Stadium, the 1980 Olympic venue, with the pool games to be completed on Saturday before the playoffs on Sunday.
In other results, Fiji, the only two-time winner, blew away Tonga 45-0 with Metuisela Talebula and Watisoni Votu scoring two tries each.
England came right in the second half to defeat Portugal 21-7.
Wales, the surprise champion four years ago in Dubai, downed Uruguay 33-5.
Host Russia was routed 31-0 by South Africa, and Philippines, the only team of the 24 making its debut, was run over by Kenya 45-5.
Canada plays its final two Pool D games Saturday against the United States and Georgia.
Canada's women's team plays all its Pool A games on Saturday against the Netherlands, Tunisia and New Zealand.