Keller made it 3-1 at 2:50 of the second, beating Ullmark from inside the left face-off circle, and Carcone cut it to 3-2 at 3:22, taking the puck away from Bruins forward Matthew Poitras before scoring.
Danton Heinen made it 4-2 at 9:12, taking a pass from Poitras and scoring from the slot.
"[Poitras] won a battle there on the wall," Heinen said. "First good reload by him, and then you know, a little chip there to me. I was lucky enough to put it in, but that was a good play by him and [Frederic] there to create all that."
Crouse cut it to 4-3 at 3:20 of the third period from the slot.
The Coyotes had two power-play opportunities after getting within one goal in the third period, but failed to capitalize, going 0-for-5 in the game.