McAvoy's tumbling wrist shot from the right face-off circle eluded Wedgewood inside the far post on a Bruins power play to make it 2-1 at 13:41 of the second period. Boston's power play has scored in eight consecutive games (10-for-25, 40.0 percent).
"We said before the game they're obviously good on special teams, so don't get their big boys going on special teams. I think we limited their chances," Gostisbehere said. "If one or two bounces goes our way, it's a different game."
The Bruins couldn't score despite getting two power plays 15 seconds apart early in the third period.
"We had some puck luck as well. They could easily have dropped in one or two goals, but they didn't," Ullmark said. "We've got to keep building off from this game."
The Bruins were coming off a 4-3 overtime loss at the Colorado Avalanche on Wednesday, when they couldn't hold a 3-1 lead in the third period.
"I thought we did a good job, it's nice to close this one out compared to what we didn't do in Colorado," Ullmark said.
Ullmark made two strong saves in the final minute after the Coyotes pulled Wedgewood to give them an extra attacker. He stopped a wrist shot by Clayton Keller with 36 seconds left and kicked out a wrist shot by Lawson Crouse with one second remaining.
"I think we played good in the third, we gave them a push, they sat back a little and trapped it up," Gostisbehere said. "We had a good chance there at the end.
NOTES: Arizona forward Johan Larsson sat out with a lower-body injury and is day to day. … Schmaltz has scored five points (three goals, two assists) in his past three games. … Wedgewood is 1-8-1 in his past 10 starts and hasn't won since Dec. 17 against the Anaheim Ducks. … Boston hasn't lost at Arizona since Oct. 17, 2009. … The Coyotes play the second of back-to-back games against the Buffalo Sabres on Saturday. … Bruins defenseman Matt Grzelcyk blocked two shots in 18:04 after missing two games with an undisclosed injury. … Coyotes forwards Antoine Roussel and Ryan Dzingel returned after each missed four games in NHL COVID-19 protocol. Roussel had four hits in 9:59 and Dzingel had two shots and four hits in 11:39. ... Boston recalled goalie Troy Grosenick from the taxi squad and he was the backup to Ullmark.