Keller got Arizona within 2-1 with one second remaining in the second period on a one-timer off Dysin Mayo's pass to the top of the right circle.
Brad Marchand had a chance to give Boston a two-goal lead early in the third period, but his shot at an open net was deflected by Mayo. Ritchie then tied it 2-2 at 2:15 by putting in Barrett Hayton's rebound for his third goal in three games.
Coyle made it 3-2 with 3:21 remaining, finishing a breakaway from his zone by switching from his forehand to his backhand as Vejmelka crowded the near post.
"It's a tie game, right, so you want to make the appropriate play," Coyle said. "There's no passing lanes, it was a bobbled puck, so I just wanted to take it to the net and create a rebound, if anything."
The Bruins' third line of Trent Frederic (two assists), Coyle (assist) and Smith scored three goals and had three assists.
"They're playing to the identity of how they would need to play to score on a regular basis," Cassidy said. "They've capitalized on the rush by not overthinking it, like the goal Charlie scored. They gave him a path to the net, they took away the pass on the 2-on-1 and he took the shot."