With Miller in the dressing room and Boston a man down for three minutes, the Bruins scored three goals in the last 13 minutes of the second - including a pair jut 1:44 apart at the end of the period - to pull away. Following the open-ice impact, Burmistrov remained motionless on the ice for several moments.
It was the 10th straight victory for the Bruins (33-24-6) over the Coyotes (22-33-7), who haven't won in Boston since 2009.
The next 20 minutes had much more action, starting with Arizona tying the game at one three-and-a-half minutes into the period when Peter Holland beat Tuukka Rask.
It took just over three minutes for the scoring to get started for the home team when Colin Miller was fed a attractive pass from David Pastrnak to light the lamp for the 1-0 lead.
Bruins: Host the New York Rangers on Thursday night.