Marc Gagnon crossed the line ahead more than five seconds ahead of Italy, with China coming home in third.
The United States finished off the pace in fourth after Rusty Smith had fallen earlier in the race.
But Canada, the gold medal winners at Nagano and the only team not to crash, had an anxious wait before their win was confirmed.
At an early change-over, China fell back after a clash of skates with the Canadians, but judges deemed it accidental.
That was the only trouble the Canadian team of Gagnon, Jonathan Guilmette, Francois-Louis Tremblay and Mathieu Turcotte experienced over the course of 44 laps.
"We were very confident of winning, but we were very tired. We really pushed and got it," Gagnon said.
The relay gold left him as the most decorated short track skater in Olympic history with five medals.
The 26-year-old had won his fourth medal, a 1,500m gold, earlier in the evening.
"I'm just glad I did all of that work and it paid off in the end. It just shows people that if you have a dream, it can come true," he added.
Like China, Italy also suffered at a change-over, losing speed following an over vigouros push exchange that saw both skaters lose their balance.
However, the surprise winners at Lillehammer in 1994, recovered and took over second when the Americans, who finished a lap down, slid into the barriers on a turn.
For Gagnon, it was a second gold of the night following his success in the 500m.