It paid off early; Markstrom made his best saves against Auston Matthews at 14:40 of the first period when he closed his pads on a redirection in tight and made another pad save on the rebound.
"It helps spending time with the goalie coach; small stuff and details that's hard to work on when you're playing every day," Markstrom said. "From puck drop to the end, I felt really comfortable."
Markus Granlund and Alexander Edler scored in the first period for the Canucks (12-10-4), who were outshot 25-9 over the final two periods.
"We got them on their heels a little at the beginning, and obviously they came hard the last two periods," Vancouver coach Travis Green said. "I was proud of how we withstood their pressure."
Frederik Andersen made 24 saves for the Maple Leafs (17-9-1), who were trying to complete a sweep of their three-game road trip through Western Canada.
"We didn't get ready and the first period cost us, spent the whole night playing catch up," Toronto coach Mike Babcock said. "We had lots of opportunity, the goaltender was good, but we weren't ready to go at the start and catch-up hockey is usually losing hockey."
Granlund made it 1-0 at 4:52 of the first period, after a turnover by Matthews just inside the Maple Leafs blue line. It was Granlund's first point in seven games.
Edler scored his first goal of the season on a delayed penalty at 11:14 of the first period to make it 2-0. Vancouver held possession of the puck for 28 seconds after the penalty was called, with Daniel Sedin and Henrik Sedin passing back and forth several times on the cycle before combining to set Edler up above the left face-circle.
"In those situations, it's a good idea to get the puck to the twins still," said Edler, who beat Andersen high over the blocker. "They will find something."