Nikolaj Ehlers scored the game-winner just 3:29 into overtime, besting goaltender Jakub Dobes for the second time on the night.
It's now Ehlers' second career playoff overtime goal and the Canes' first Eastern Conference Finals home win since June 1, 2006.
Carolina goaltender Frederik Andersen only needed to record 10 saves for the game, now marking the ninth time out of 10 games these playoffs he's allowed two or fewer goals.
The series now heads north to Montreal for Game 3 (May 25th) and Game 4 (May 27th).
Recap & Highlights
It took less than two minutes and the game's first shot on goal to see a change on the scoreboard.
Eric Robinson scored his second goal of the playoffs to give Carolina an early 1-0 lead in Game 2. Both of his goals have come from this series against the Habs.
William Carrier and Mark Jankowski both picked up their second assists of the postseason on the goal.
Exactly six minutes later, the Habs would go on the game's first power play, but couldn't capitalize on the man-advantage.
They preferred even strength after Josh Anderson scored his fourth of the postseason to tie things up 1-1, less than a minute after their power play ended.
Phillip Danault (7) and Kaiden Guhle Stats (8) picked up the assists.
Entering the first intermission, the Canes outshot (7-2) and outhit (13-6) the Habs. Montreal would enter the locker room with little remaining on their second power play of the game.
They dodged a bullet in the remaining seconds of the first as the Canes saw a 2-on-1 opportunity for a short-handed goal, but Seth Jarvis, who scored the first goal of the series, whiffed on the shot attempt.
But with under three minutes left, and another failed power play opportunity later, the Canes would retake the lead.
Ehlers scored a beauty for his third of the postseason to make it a 2-1 game. Jacob Slavin and Jalen Chatfield both recorded their second assists of the playoffs.
Following a penalty right before the end of the second period, the Habs entered the third with just a total of five shots on goal, down a man, and were outhit 35-15.
Alexandre Texier received a minor for slashing after hitting K'Andre Miller in the groin, which some argued should've been a five-minute major.
With under eight minutes left to go in the third, the Habs found their way into the back of Carolina's net for the second time on just their ninth shot on goal for the game.
After only scoring 13 times during the regular season, Anderson scored his second of the game, fifth of the playoffs, to tie the game 2-2 for Montreal.
Alexandre Carrier picked up his sixth assist of the playoffs, while Denault recorded his second of the game and eighth total.
Montreal put up seven shots on goal in the third, which was more than their previous two periods combined. However, the Canes would still outshoot them 24-12 and outhit them 44-16 heading into OT.
From there, it was Carolina who prevailed in the end as the series heads to Game 3. Both teams finished a combined 0-for-5 on the power play, with no penalties being called in the third period or overtime.