Charlie Coyle had given the Bruins a 4-3 lead at 16:09 with a one-timer off a pass from behind the net by James van Riemsdyk.
“It’s a shame we couldn’t pull it off,” Coyle said. “We had a couple of third-period leads and we can’t afford to give those up. Good teams are going to keep battling like that, but we’re a good team too. We have to make sure that we play the right way and are doing the right things, especially with a lead.”
Tanner Jeannot put the Lightning up 1-0 at 6:39 of the first period when he charged the net and lifted a rebound over Swayman’s pad.
Pavel Zacha tied it 1-1 at 9:55 at the side of the net off a pass from Pastrnak after Boston forced a turnover on the forecheck.
Nicholas Paul put Tampa Bay ahead 2-1 with a power-play goal at 19:30 of the second period, redirecting a shot from Mikhail Sergachev.
“The effort level from the guys these last few games … they’re being rewarded for it,” Cooper said. “It’s not always perfect … but I’m just really happy for the guys.”
Pastrnak tied it 2-2 at 6:26 of the third with a shot from the point through traffic that beat Johansson to the glove side.
John Beecher gave the Bruins a 3-2 lead at 7:47 when he scored from the high slot after forcing a turnover.
“I loved how resilient we were,” Montgomery said. “We just kept coming back. The belief on the bench was always that we were going to be able to win that game.”