With the result, both teams have managed to win one game at home, and one of the road so far in the series.
The game's opening goal came 6:32 into the first period, when Mattias Samuelsson recieved the pass from Josh Norris to hit a first-time shot into the back of the net.
The Habs were fortunate not to go down 2-0, as Jack Quinn thought he doubled Buffalo's lead. However, after a coach's challenge, the goal was called back due to goaltender interference.
Montreal made the most of their reprieve as they tied things up. Jake Evans' initial effort went just wide of the goal, but he stuck with the play as he found Alex Newhook. The 25-year-old made no mistake in beating Ukko-Pekka Luukkonen.
It was Newhook's fifth goal in his last three games.
There were several power plays in the opening frame, and the Canadiens managed to make the most of one seconds before the intermission. Cole Caufield received the puck on the wing, closing in on goal. While Luukkonen had his angle covered, Caufield made a move inwards before firing it in the opposite side to score.
Although they had more shots on goal in the first 20 minutes, Buffalo found themselves behind.
The Sabres found their leveller through a power play of their own, as Alexandre Carrier was penalised for a high stick. On the ensuing man advantage, Tage Thompson scored one of the strangest goals of the playoffs when his clearance hit the back wall and found a way in as it hit Jakub Dobes in the Montreal net.
That was the only goal of the middle period, where the Habs dominated proceedings for much of the frame.
The game winner came with 13 minutes left, and once again, a power play proved key. Receiving the puck in front of goal, Zach Benson converted a backhand to score what proved to be the winner.
Much of the remaining time in regulation saw the Habs try to find another goal to tie things up. They did throw on a sixth attacker towards the end, but it proved to no avail.
The series will head back to Buffalo for Game 5 in what has in essence become a best-of-three.