Halak is 4-0 with a 1.75 goals-against average and .936 save percentage since Tuukka Rask opted out of the Stanley Cup Playoffs on Aug. 15.
"We've got to help him out, but we also have so much confidence in him," Bruins forward Charlie Coyle said. "He's a great goalie. He's been huge for us. When they slip in there and we break down a little bit, he's there to shut the door."
WATCH: [All Bruins vs. Lightning highlights]
Brad Marchand and David Pastrnak each had a goal and an assist for the Bruins, the No. 4 seed in the East, who have won five of their past six games after going 0-3-0 in the round-robin portion of the Stanley Cup Qualifiers.
"We obviously buckled down when the playoffs started," Marchand said. "That's kind of how the script is. When it's time to play, guys are prepared and know how to prepare. It kind of showed tonight. But it's one game. We have to follow it up next game."
Victor Hedman scored twice and Andrei Vasilevskiy made 28 saves for Tampa Bay, the No. 2 seed, which was 0-for-3 on the power play after failing to score on each of its 10 opportunities against the Columbus Blue Jackets in the first round.
"It hasn't burned us yet, but if it continues, it very well might," Lightning coach Jon Cooper said. "You get down to those one-goal games, usually it's the special-teams goal that's going to get you. They got theirs (Boston was 1-for-3) and we didn't get ours. … I'm not sitting here blaming the game on special teams by no reason, but it's an area that we have to improve at in this series."
Teams that win Game 1 are 485-220 (68.7 percent) winning a best-of-7 NHL playoff series, including 7-1 in the first round this season.
Game 2 of the best-of-7 series is in Toronto, the Eastern hub city, on Tuesday (7 p.m. ET; NBCSN, CBC, SN, TVAS).
Coyle put the Bruins ahead 1-0 at 18:52 of the first period when he deflected a shot from Brandon Carlo.
Pastrnak made it 2-0 with a power-play goal at 4:34 of the second period, scoring on a one-timer from the left face-off dot off a cross-ice pass from David Krejci.
Krejci has 10 points (three goals, seven assists) during a seven-game point streak.
Marchand extended the lead to 3-0 at 1:17 of the third period. He scored on a one-timer off a backhand pass from Pastrnak, who got the puck after Patrice Bergeron forced a turnover by Lightning defenseman Ryan McDonagh.
"You're typically not going to advance if your best players aren't your best players," Bruins coach Bruce Cassidy said. "Their line carried us. I thought some other guys did their job as well, just didn't get rewarded on the scoresheet. But a nice start for that line."
Hedman made it 3-1 at 8:50 of the third on a shot from above the circles, Tampa Bay's first of the period, before cutting it to 3-2 with 1:14 remaining and Vasilevskiy pulled for the extra skater.
Each of Hedman's goals redirected in off Boston defenseman Charlie McAvoy.
"We want to have that shooter mentality," Hedman said. "We work on it a lot in practice. When we get big bodies in front, it's tough for the goalie to see the puck. So it's an onus on us D-men to get pucks through. We've got to keep doing that. We know what works. We know what's going to give us success."
The Lightning outshot the Bruins 27-16 in the final two periods after being outshot 15-10 in the first.
"We have to adapt and do a few different things," Tampa Bay forward Tyler Johnson said. "I thought in the first period, the main thing was our heads weren't quite into it. Our legs weren't going."
Notes: McDonagh left midway through the third period for undisclosed reasons. No update was provided. … Vasilevskiy made his 37th start in the playoffs, passing Ben Bishop for the most in Lightning history. … Marchand has 92 points (34 goals, 58 assists) in 117 playoff games, tying him with Bobby Orr, who had 92 points (26 goals, 66 assists) in 74 playoff games, for seventh in Bruins history. … Pastrnak has four points (one goal, three assists) in two games since returning from being unfit to play in Boston's previous three games.
NHL.com staff writer Mike Zeisberger contributed to this report
