David Pastrnak gave the Bruins a 1-0 lead at 3:07 of the first period. Torey Krug passed to a cutting Pastrnak, who beat Vasilevskiy with a backhand at the left post.
David Backes scored a power-play goal at 10:54 to make it 2-0. After Krug's shot from the point went wide, Backes gathered the puck in front of the net and his shot deflected off Lightning defenseman Dan Girardi.
"Tough, it's frustrating," Tampa Bay defenseman Anton Stralman said. "It's tough to live with right now because we're trying to become a better PK unit."
Riley Nash scored a power-play goal on a rebound from in close at 12:33 of the second period to extend the lead to 3-0.
"I thought that was one of our best performances top to bottom, goalie, defense, forwards with everybody contributing," Nash said. "It felt like a playoff game out there, a lot of intensity. The crowd was in to it. … It was physical, and it was just a fun game to be a part of."
Backes left the game with 22 seconds left in the first period with a laceration above his right knee, but Cassidy said there was no structural damage.
"Obviously there is concern going forward about swelling or infection," Cassidy said. "I don't want to say he dodged a bullet because it's an unfortunate accident, but it looks like he'll be OK. From there I don't have an update. We'll see how it looks [Sunday].
The last time the Lightning were shut out at Amalie Arena was March 16, 2017, a 5-0 loss to the Toronto Maple Leafs.
"Best defensive game in a while tonight throughout the lineup," Rask said. "Our [defensemen] were fantastic today breaking pucks out, blocking shots, making plays, and the forwards helped out coming back to shut down the slot area and not give up many chances from there. It's a great example of when we put our minds to it how good we can be."
