Boston (34-10-12) has won its past 16 games against Arizona (27-23-7). The Coyotes last defeated the Bruins on Oct. 9, 2010 in Prague.
Charlie Coyle scored two goals for Boston, and Rask extended his home point streak to 18 games (12-0-6), passing Gilles Gilbert (16 wins with one tie to start the 1973-74 season) for the longest run by a Bruins goalie to begin a season.
"I think we play like a good team at home and we battled back from some multigoal deficits in the third period," Rask said. "I think that just shows how resilient we are as a group. And you know I just try to give us a chance to win and just work to get a point at least."
WATCH: [All Coyotes vs. Bruins highlights]
Adin Hill, who was named Arizona's starter just before game time because of a lower-body injury to Antti Raanta, made 29 saves for the Coyotes, who started a four-game road trip by losing for the seventh time in their past eight games (1-5-2).
"We played hard. They had a couple of, two or three power-play goals, couple of fluky ones," Arizona coach Rick Tocchet said. "Tough one. But I thought we played hard, had a couple of looks there to tie it. You know, proud of the way we played. Tough circumstances, we played a good game."