Trailing 3-1 midway through the third period, Boston faced the prospect of going back to Montreal trailing the Canadiens 2-0 in the series.
But the Bruins responded with three goals in under six minutes to even up the 34th post-season meeting between the rivals.
Montreal tied the game just over a minute in the second period. A Brad Marchand turnover in the neutral zone resulted in a scramble in front of Boston goalie Tuukka Rask, with defenceman Mike Weaver eventually scoring.
Vanek and Subban teamed up for another power-play goal at 6:30 of the third period when Subban's shot from the blue-line on was tipped in by Vanek.
Bruins defenceman Dougie Hamilton made it a one-goal game at 10:56 when his snap shot picked the top-left corner of the Canadiens' goal.
Smith scored with 3:32 left to complete the comeback, putting the puck over a fallen Carey Price.
Milan Lucic added an empty-net goal.
The series now switches to Montreal with Game 3 scheduled for Tuesday at the Bell Centre.