Rask made 26 saves but fell one game short of the Boston record with his first regulation home loss this season (14-1-6). The NHL-leading Bruins (39-13-12) have lost two straight and had their home winning streak end at seven.
"I mean the second period wasn't really our strongest," Rask said. "I think the third we picked it up and played with our pace and structure, got some chances."
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Mikael Backlund had two goals and an assist, Sean Monahan scored twice, and David Rittich made 26 saves for the Flames (33-25-6), who have won three of four and are 6-3-0 in their past nine games. Calgary holds the first wild card into the Stanley Cup Playoffs from the Western Conference.
"This shows not just ourselves, the whole League, that we're a really solid team," Backlund said. "And we've known that all year. It's been a lot of ups and downs ... we know we have to be more consistent. But when we play the right way, we're really, really a dangerous group."
Matthew Tkachuk gave the Flames a 1-0 lead at 11:35 of the first period. After Backlund's one-timer rebounded off the end wall, Tkachuk scored on a backhand shot.