He said the win was special because it came 40 years after Canadian Gilles Villeneuve had won his first race for Ferrari.
It was the first win by a Ferrari on Circuit Gilles Villeneuve since Michael Schumacher's triumph in 2004.
The four-time champion German drove his Ferrari with near flawless aplomb to convert his 54th pole position into a triumphant afternoon ahead of Finn Valtteri Bottas of Mercedes and determined Dutchman Max Verstappen, who was third for Red Bull.
Formula One race director Charlie Whiting said the error was caused by simple miscommunication between the official starter and crew in the starter's tower, which resulted in model Winnie Harlow - a friend of Mercedes world champion Lewis Hamilton - waving the flag prematurely.
"We got pole today for a reason", said Vettel.
The team took some time to find its pace over the weekend with Vettel not fully at ease with the vehicle until qualifying when he found the set-up he wanted to deliver an impressive pole, from which he dictated the race and converted into an equally impressive win.
Stroll, 19, was in is second Canadian GP.
His engine was six races old but Hamilton would have expected better.
"The team has been extremely strong in the past at keeping reliability on a high level so that is not a part that worries me, it is more we have seen today a Ferrari that is the stronger vehicle - strong in qualifying, strong in race and at no time we had a chance to fight for the win".
Mercedes were never in the victory equation, having not got engine updates ready in time for the race while Ferrari and Red Bull both had new parts. That might provide an internal headache for Red Bull, a team that has been known for financially rewarding its drivers for claiming the fastest lap of the race.
Daniel Ricciardo was in P4 after keeping Hamilton off his tail. "We've seen this year it's very close between the three teams and the six drivers so we'll see, but for sure if you start on pole you want to win". "In the race, it all calms down a bit so that's why I think we're always a bit more competitive in the race".
Ferrari's Kimi Raikkonen was sixth, and said it had been a boring race, with Renault's Nico Hulkenberg and Carlos Sainz seventh and eighth.
Fernando Alonso would have hoped to make Q3 in his 300th Grand Prix weekend, but he had to settle for P14 after finishing Q2 more than a second off the pace.
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