But it came at a cost after Ismael Kone suffered a broken leg and had to be strechered off.
The Canadians started the home tournament with a 1-1 draw against Bosnia and Herzegovina but bouced back in the best possible way on Thursday.
They led 2-0 by the half-hour mark thanks to goals from Cyle Larin and Jonathan David.
Qatar had their first player sent off in the 33rd minute. Homam Ahmed tripped Tajon Buchanan and the referee initially awarded Canada a penalty.
After video review the decision was overturned, while Ahmed's yellow card was upgraded to a red.
Before the break, David scored his second to give Canada a comfortable 3-0 lead.
Things were looking great for the co-hosts but there was a scary moment in the 52nd.
Ismael Koné went down after a challenge with Assim Madibo. He was conscious but had to be carried out on a stretcher, while Madibo received a red card as Qatar went down to nine players.
Canada coach Jesse Marsch admitted the squad had been shaken by Kone's injury.
"I haven't spoken to Ismael yet, he's at the hospital, he will prepare for a surgery. I'm going to see him after this press conference.
"We'll see exactly what we decide to do for him. His family is with him at the hospital. It happened right in front of the bench - everyone could hear the bone snap.
"Your heart goes out to him, and everybody's a little shaken by the experience, because of the nature of the injury and also because Ismael is a big part of the team."
From then one, things got easier for Canada with the red card. Nathan Saliba in the 64th and Mohamed Manai's own goal in the 75th sealed the win before David completed his hat-trick in stoppage time to crown an otherwise fantastic day in Vancouver.
Marsch was upset by the reaction from the opposition bench after the red card was shown.
Marsch and his Qatar counterpart Julen Lopetegui had a testy exchange after the match, but neither man wished to divulge the details.
"I'm not spending one second (discussing it), it's not worth any of our time to discuss," Marsch said.
Lopetegui insisted there was no "intention" of Madibo to injure Kone, adding: "First of all I want to wish all the best to Kone and to recover as soon as possible. I wish all the best to him."
Canada now top Group B on goal difference but are tied with Switzerland on four points. The Swiss team earlier defeated Bosnia and Herzegovina 4-1.
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