The pair of goals for Bergeron and Nash gave each three total in the playoffs. Jake DeBrusk (6th playoff goal) and Brad Marchand (4) also scored and Tuukka Rask finished with 34 saves for the Bruins. David Pastrnak added a career-high four assists.
"We were resilient today," Rask told NBC after the game. "We weathered the storm in the first (period). We knew they were going to come out hard and we capitalized on our chances. I think we defended pretty well, for the most part."
Mikhail Sergachev (2) and Dan Girardi (1) scored the goals for Tampa Bay. Andrei Vasilevskiy had 18 saves for the Lightning.
Game 2 is Monday night in Tampa.
Boston defeated the Toronto Maple Leafs in a seven-game, first-round series to set up its meeting with Tampa Bay. The Lightning ousted the New Jersey Devils in five games in their opening-round series.
The Bruins outscored the Lightning 10-8 in winning three of their four regular-season games.
Tampa Bay won the Atlantic Division and finished with the best record in the Eastern Conference standings, one point ahead of Boston. The Bruins would have won the division with a win against the Florida Panthers in the regular-season finale.
Nash's power-play strike opened the scoring at 17:11 of the first period.
Bergeron made it 2-0 when he scored 42 seconds into the second period, but Girardi's goal at 2:31 gave Tampa Bay life. Nash's second goal at 12:33 of the middle period made it 3-1.
Sergachev's power-play goal at 13:22 of the second brought the Lightning within 3-2.
The goal came after Bruins goalie Rask lost the blade on his left skate in the middle of the play, hindering his lateral motion. After the play, Rask pleaded his case to the referees and threw the loose blade against the boards in frustration.
"I was yelling at the ref for like 10 seconds -- he didn't hear me," Rask said. "It sucks, but glad we won."
Marchand struck 3:32 into the third and Bergeron added some insurance at 10:11 of the period.
DeBrusk tacked on an empty-net goal with 6:19 remaining.
--Field Level Media
Boston | Tampa Bay | |
Brad Marchand 4 | Points | Dan Girardi 1 |
Patrice Bergeron 2 | Goals | Dan Girardi 1 |
David Pastrnak 4 | Assists | Yanni Gourde 1 |
Rick Nash 1 | Power Play Goals | Mikhail Sergachev 1 |
N/A | Short Handed Goals | N/A |
Tuukka Rask .944 | Save Percentage | Andrei Vasilevskiy .783 |
Tuukka Rask 34 | Saves | Andrei Vasilevskiy 18 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Boston | 24 | 6 | 1-1 | 2-3 | 6 | 25 |
Tampa Bay | 36 | 2 | 1-3 | 0-1 | 2 | 26 |