Montreal, which took the first two games in Boston, still leads the best-of-seven Eastern Conference quarter-final 2-1 with Game 4 set for Thursday night at the Bell Centre.
Chris Kelly ended the drama with an empty-net goal with 36 seconds left to play.
Montreal outshot the Bruins 36-25 on a tough night for Canadiens goalie Carey Price.
The crowd of 21,273 was roaring before the game even started, sparked by an appearance by legendary captain Jean Beliveau holding a torch. But it was the Canadiens who looked to be lacking focus against a closer checking Boston team than they had faced thus far in the series.
For the first time in the series, the Habs failed to get an early goal. Boston opened the scoring at 3:11 of the first when Patrice Bergeron set up Krejci in the slot to bury the Bruins' first shot of the game.
Price was the culprit as Boston made it a three-goal lead 2:02 into the second. His clearing pass was picked off and Peverley shot into the open net.
But the Bell Centre came to life as Kostitsyn, back from missing a game with a foot injury, undressed Chara on a rush and slid the puck between Thomas' pads at 7:03.
Montreal cracked up its intensity in the third and Plekanec scored at 4:08 when, on a rush against Chara, he spun and fired a shot along the ice that again went in between Thomas' pads.
Chara, who returned after missing Game 2 with dehydration, played his first game in Montreal since his controversial hit March 8 that left Habs winger Max Pacioretty with a concussion and a fractured vertebra.
The Bruins captain was booed loudly every time he touched the puck, but he got the same treatment even before the Pacioretty incident. Chara was used heavily on the night, but was not at the top of his game.
Notes: With Kostitsyn back, Yannick Weber was dropped despite having scored in Game 2. ... Chara bumped Shane Hnidy out of the lineup. ... One goal in the first two games was Boston's lowest total since it was shut out twice to start a 1995 series against New Jersey. ... The Bruins will spend two days in Lake Placid, N.Y., and return to Montreal on Wednesday night.