William Nylander had a goal and two assists, John Tavares had a goal and an assist, and Jack Campbell made 32 saves for Toronto, the No. 2 seed in the Atlantic Division.
Steven Stamkos and Victor Hedman scored, Nikita Kucherov had two assists, and Vasilevskiy made 21 saves for Tampa Bay, the No. 3 seed in the Atlantic.
The Lightning are 16-0 since the beginning of the 2020 Stanley Cup Playoffs following a loss.
"We're here to win the series," Tampa Bay coach Jon Cooper said. "We lost a game tonight; we let this one slip away, that's on us. But we haven't let the series slip away; we let a game slip away so that's how you look at it. Play it game by game."
RELATED: [Complete Maple Leafs vs. Lightning series coverage]
Stamkos put the Lightning up 1-0 5:19 into the game when he shot from the slot past Campbell's blocker.
Hedman made it 2-0 at 6:11 when he took a pass from Kucherov and shot from the high slot on the power play.
Toronto killed off a 30-second 5-on-3 power play beginning at 11:17 when Mark Giordano was assessed a minor penalty for cross checking with Nylander already in the penalty box for holding.
The Lightning outshot the Maple Leafs 14-4 in the first period.
"We knew that they were going to push and you have to give them credit," Stamkos said. "It was a tremendous start for us, the start we wanted. It's usually one of those bad omens when you get an extended 5-on-3 and you don't score, I always say that's kind of a rule. It wasn't for lack of looks, we had some unbelievable looks and that could kind of ice the game early, go up 3-0 so I was disappointed that we didn't execute. We just sat back too much and got away from our game plan."