The shutout was Vasilevskiy's first of the season and 13th of his NHL career. Nine of his shutouts have come on the road, one behind Ben Bishop's Lightning record.
"He was seeing the puck," Lightning coach Jon Cooper said. "He was great. He was making plays and coming out of the net and making the plays. He was seeing everything and seeing his rebounds.
"That was a good one. It was just fun to be a part of and have the seat that I have to watch it."
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Avalanche forwards Nathan MacKinnon and Mikko Rantanen didn't have a point, ending their season-opening streaks at nine games. They share the Colorado record with defenseman John-Michael Liles, who did it in 2010-11.
"We were battling hard, but they played a really good game," Rantanen said. "Give them credit. There are some things we could have done better, but it's over."
Nikita Kucherov scored the only goal of the game on the power-play goal at 6:24 of the third period. Steven Stamkos passed across to Kucherov in the right circle for a shot that went inside the near post. It was Kucherov's third goal of the season and 150th of his NHL career, tying Brad Richards for fourth on Tampa Bay's all-time list.
"Felt good," Kucherov said. "[Stamkos] is a skilled player. He's definitely able to do these plays. When everybody expects him to shoot, it makes it easier for us to get open. All I had to do was get open. I was sure he would make it. He's a star in this league and it's just fun to watch."