Heinen gave Boston a 2-1 lead at 15:36, scoring into an open net following a redirection in front, and Marchand extended the lead to 3-1 at 18:59.
DeBrusk scored on a redirection in front at 18:06 of the second period to push the lead to 4-1, but Keith cut it to 4-2 on a slap shot at 19:37.
Erik Gustafsson scored from the left circle at 4:48 of the third period to make it 4-3. Kane, who had the secondary assist on the goal, has 32 points (11 goals, 21 assists) during his point streak and also extended his assist streak to 14 games, tying Stan Mikita for longest in Chicago history.
Peter Cehlarik's power-play goal gave the Bruins a 5-3 lead at 7:18, and Krejci scored his second of the game at 15:42 to make it 6-3.
Bruins goalie Tuukka Rask made 23 saves and is 10-0-2 in his past 13 starts.
"I think our team has played great," Rask said. "I think I haven't like stole games. It's (not) like I've been unbelievable, it's just I've felt good, try to be there when the team needs me, but I haven't felt anything different during these games. I think we've played great hockey as a team."