Stamkos scored his 21st goal of the season and 297th of his career with Toronto defenseman Roman Polak in the penalty box for delay of game. Defenseman Anton Stralman made a pass from the point to the left circle, where Stamkos beat Bernier with a one-timer.
"We felt prepared coming into the game and had good energy," Maple Leafs coach Mike Babcock said. "We took a penalty, a tough penalty right away, and he shot it in the net how many seconds later? And then we were a little bit unraveled."
The Lightning continued to create scoring opportunities and held a 17-1 shot advantage 13 minutes into the first period, but Bernier kept his team in the game.
"For a period we really attacked tonight," Lightning coach Jon Cooper said. "It was just a continued barrage, and we stopped."
The Maple Leafs dominated the second period, outshooting Tampa Bay 11-5. Their best chance came during a power play when PA Parenteau was alone in front, but Vasilevskiy made a glove save from point-blank range.
"Our game turned at the start of the second period, we had puck possession the whole time and we got one shot," Cooper said. "We took our foot off the gas, and remember you're playing another team that wants to win and is battling their tail off, and eventually things turn. That's what happened. We got a little casual, a little cute, we tried to pass the puck into the net instead of shooting, and that's what happened."
Toronto forward Leo Komarov said the Maple Leafs have to cash in on their opportunities.
"We had a lot of chances and just couldn't get the puck in the net," Komarov said. "Their goalie played good, he's a good goalie, but when we have chances we need to score too. When you score one you get more confidence but we've had three goals in our last three games. It's tough."
Toronto continued putting pressure on Vasilevskiy in the third period, outshooting the Lightning 13-7, but he made saves on two one-timers in the slot from defenseman Dion Phaneuf and stopped a breakaway by Rielly.