Brad Marchand scored for Boston, which has won its first two games of the season. The Bruins haven't lost to Arizona since Oct. 9, 2010, the longest current streak against one opponent in the NHL.
The Coyotes, who were shut out in their home opener despite having 10 of the game's first 11 shots, have scored one goal in two games; they lost 2-1 at the Anaheim Ducks on Thursday.
"If you get tested early on, you know, you stay focused more and that's what happened," Halak said of getting pressured early in the game. "We kind of gave them a little bit more than we wanted to, but we were working on getting back and not giving them any second chances."
WATCH: [All Bruins vs. Coyotes highlights]
Halak is 10-3-2 with two shutouts in 15 games against Arizona. The shutout was the 48th of his NHL career.
"I thought he was unreal," Coyotes coach Rick Tocchet said. "We did everything right except score."
Marchand scored at 18:41 of the first. Patrice Bergeron won a puck battle along the boards and made a backhand pass to the left circle, where Marchand put a wrist shot past Darcy Kuemper (24 saves).
"I didn't see anything. I just tried to get it on net, and it found its way," Marchand said.
Bruins coach Bruce Cassidy said he liked how his top line of Marchand, Bergeron and David Pastrnak played in generating nine of Boston's 25 shots.
"Our top line was much better than they were in [a 2-1 win against the Dallas Stars on Thursday] in terms of generating offense," Cassidy said. "We just have some offensive issues right now. But I think our commitment to winning is playing the right way when we're ahead late. We didn't do anything to hurt ourselves."