DeBrusk extended the lead to 2-0 at 2:45, getting a rebound in the crease off a rush with Brad Marchand.
"We talked about having a good start and obviously, we didn't come out the way we wanted," Ekman-Larsson said. "We got down two goals pretty quick and it's tough to get back in this League when you get down like that. I think that's something we learned."
Matt Grzelcyk appeared to make it 3-0 at 17:26, but Coyotes coach Rick Tocchet challenged for goaltender interference, and the call was reversed after a video review.
"The first period we weren't ready to go, we weren't strong on pucks, we weren't finishing checks and it ended up costing us the game," Richardson said.
Richardson cut it to 2-1 at 9:10 of the second period, scoring off Vinnie Hinostroza's pass from the slot at the left post during a stretch when Arizona outshot Boston 19-1.