Tkachuk cut the lead to 3-1 with a power-play goal at 12:19. It ended an 0-for-13 drought spanning five games.
"Lots of shots, not a ton of chances, but they capitalized on theirs early, and when you get behind 3-0 against a team like that, all of those guys have been there before, in the Stanley Cup Finals, or at least most of them know how to win," Tkachuk said. "They played a solid game once they got the lead."
Curtis Lazar made it 4-1 at 2:57 of the third period on a second rebound after Trent Frederic's first two chances off the rush. Lucic's centering pass deflected off Monahan's skate at 18:24 for the 4-2 final.
"A lot of heart. A lot of heart," Ullmark said. "We grinded it out, and whenever we had the opportunity to put one in we did it. We capitalized on our chances, and that's what got us the win tonight."
NOTES: Boston is 11-0-0 when leading entering the second period. ... With his 554th assist, Bergeron moved ahead of Phil Esposito for fourth Bruins history. He extended his point streak to three games (one goal, three assists). ... Flames forward Elias Lindholm had a four-game point streak end (two goals, two assists).