The Lightning also lost two of their best players, including leading scorer Steven Stamkos, to injury in a four-minute span of the second period. After the game it was announced Stamkos suffered a broken tibia and will be out indefinitely.
The Bruins scored goals 20 seconds apart shortly after Stamkos and defenseman Sami Salo were injured, and goaltender Tuukka Rask continued his dominance of the Lightning with 28 saves in a 3-0 Boston win at TD Garden.
Rask now has a .988 save percentage (83-for-84) against the Lightning through three games this season and both of Rask's shutouts have come against Tampa Bay. Even after the shutout, the Lightning ranked eighth in the League in goals scored per game.
"I think as a team we've played pretty good against them, and it helps my job a lot," said Rask, who has a .967 save percentage and is 3-0-1 in his last four games overall. "Obviously they get chances, but it's not like they get chances all the time. So I think [some] of the best games we've played as a team has been against these guys."
Tampa Bay goaltender Anders Lindback made 23 saves on 25 shots.
The Bruins (11-5-1) have now won three in a row. The Lightning (12-5-0) had their four-game winning streak snapped.
"I think our team's playing better all the time," Bruins coach Claude Julien said. "I think we looked more like the team we want to be tonight. And we played a pretty good team and I thought our guys handled themselves well."
Stamkos, who is tied for the NHL lead with 14 goals and 23 points and had been on a six-game goal streak, was injured at 12:49 after some contact in front of the Tampa Bay net with Bruins defenseman Dougie Hamilton.
Stamkos slid into the right post and seemed to hit his right leg. The Lightning star attempted to get up and skate but immediately fell back down and began punching the ice with his right fist before he was attended to by medical personnel. He was removed from the ice on a stretcher.
Salo was then injured after a hit by Bruins forward Carl Soderberg behind the Tampa Bay net. Salo left the ice favoring his right leg.
"We went 16 games without anybody being hurt and the snowball went down the hill today," Lightning coach Jon Cooper said. "It was a little tiny guy and it ended up a mountain when it got to the bottom of the hill. Again, I don't know the prognosis on all these guys, but you lose nobody for 16 games and you lose three games in one, that's tough.
"And it's hockey. Everybody loses guys. Just pick a team. Everybody's lost players. Ours just happened all at once and you can't hang your head. You know it's going to happen at some point. That's why you have depth in the organization and we'll see where we're at."
Seconds after Salo went down, the Bruins turned an Ondrej Palat wide shot into a goal. Marchand tracked the loose puck to the neutral zone and led Boston's attack. Marchand hit Torey Krug for a shot from the high slot. The puck was knocked down and Patrice Bergeron banged it into the goal at 17:09 for a 1-0 lead.
Twenty seconds later, the Bruins doubled their lead. Under pressure from Bruins forward Daniel Paille at the right point, Tampa Bay defenseman Keith Aulie misplayed his attempt to intercept Gregory Campbell's chip up the wall. Paille skated out of the zone with the puck and went in on a 2-on-1 with linemate Shawn Thornton. With Thornton driving the net, Paille kept the puck, cut to the slot and beat Lindback with a backhand shot for a 2-0 lead at 17:29.
Aulie went to the dressing room early in the third period because of an upper-body injury, leaving the Lightning with 15 players. Jarome Iginla's empty-net goal with 58.7 seconds remaining provided the Bruins their final margin of victory.
Lightning captain Martin St. Louis didn't want to blame the injuries for the goals his team gave up or its inability to make a comeback.
"I don't think so," St. Louis said about the injuries deflating the team. "We had chances. We had chances too. We just didn't put the puck in the net."
The Bruins extinguished all four Lightning power plays in the game to run their success streak to 22 straight kills over the past eight games.
Tampa Bay's last win against Boston was March 13, 2012. The Lightning's last win at the Garden was March 25, 2010.
The Bruins will conclude their season-long five-game homestand Thursday against the Columbus Blue Jackets. The Lightning's three-game road trip concludes against the Montreal Canadiens on Tuesday night.