Jonathan David was the hero, completing a hat-trick in a game that Qatar made progressively easier for the home side by finishing with nine men.
Cyle Larin opened the scoring in the 16th minute, following up after David's shot had been parried to the feet of the Besiktas striker. David doubled the lead at the end of the first half after Qatar's Homam Ahmed was shown a straight red card for denying a clear scoring opportunity.
The second half turned uglier when Assim Madibo lunged into Koné and left the Canadian midfielder writhing on the ground with what appeared to be a serious leg injury. Players from both teams were visibly shaken as Koné was stretchered from the field to a standing ovation from the crowd, which included an emotional Canadian bench. Madibo received a second red card for Qatar, reducing them to nine men.
Substitute Nathan Saliba, who came on for Koné, scored almost immediately with a free kick and held up his injured team-mate's jersey in celebration.
Qatar conceded a fifth when Mohamed Manai turned the ball into his own net in the 75th minute, and David completed his hat-trick in the second minute of stoppage time, intercepting a shot and finishing left-footed.
Canada controlled possession for close to 80 per cent of the match and were never threatened. The 6-0 margin is the largest winning margin at this tournament, matched only by Germany's 7-1 over Curacao on goal difference.
Canada top Group B on four points alongside Switzerland, both unbeaten through two matches, with the co-hosts now needing only a point from their final group game to guarantee a place in the last 32 for the first time in their history.
The news on Koné's injury is what Canada will be most anxious to hear first.