Seth Jarvis scored the game-winner for the Hurricanes as the series now heads to Las Vegas for Game 3 on Saturday, June 6th.
Shayne Gostisbehere picked up his second assist of the game, along with Sebation Aho's first.
Both teams had 26 shots on goal, but Carolina goaltender Frederik Andersen held out for just one more save than Vegas' Carter Hart to make it a 1-1 series.
This now marks eight-straight playoff overtime wins for the Hurricanes dating back to Game 5 against the New Jersey Devils in 2025.
It is also the second time in the history of the NHL where a team has completed a multi-goal comeback in the first two games of the Stanley Cup Final. The other was done by the Los Angeles Kings in 2014.
Recap & Highlights
In what looked like a dominating start by the Hurricanes, it was the Golden Knights who came out of the first period with a 1-0 lead with just two shots on goal - the fewest in a period by Vegas all postseason.
Brett Howden scored his 12th goal of the postseason after fighting through Carolina defenders to beat Andersen.
It also marked just the third time this postseason that Carolina has given up the first goal of the game. The previous two were against the Philadelphia Flyers in Round 2 (Games 2 & 4), both of which the Hurricanes won in overtime.
Meanwhile, Mitch Marner, who picked up his 16th assist of the postseason, tied Alexander Ovechkin for the second-most points (16) in a player's first 10 road playoff games for one franchise.
The assist put him just three points short of the legendary Wayne Gretzky (19). He'll also need four more total points this postseason to surpass current teammate Jack Eichel (26P) for most by a Golden Knight ever in a single postseason run.
Heading into the first intermission, Carolina outshot Vegas 27-8 (8-2 on goal) and had 11 scoring chances to just the two for Vegas.
Brayden McNabb would leave the game in the first period and was rushed to the hospital for further evaluation after taking a puck directly to the face.
But coming out of the locker room, the Golden Knights couldn't have cared less about the stat sheet and made up for a big loss in McNabb being ruled out.
And who else to double Vegas' lead but Howden with his second of the night to put them up 2-0.
With his 13th goal of the postseason, Howden now needs just one more to surpass Jonathan Marchessault (13) for the most in a single playoff run in Vegas' young history.
Howden is now the first player in NHL history to score a dozen or more goals in the regular season, then surpass that amount in the playoffs (he scored 12 in the regular season).
Ivan Barbashev (8) and Nico Hanafin (7) picked up the assists.
Vegas turned the tables in the second period, heading into the locker room for the second time outshooting Carolina 9-7.
The Golden Knights failed on both of their power plays in the second frame, with both teams entering the third period going a combined 0-for-5.
Carolina finally found some life from their playoff star to cut Vegas' lead in half.
Logan Stankoven scored his 10th goal of the postseason to make it a 2-1 game with just under 10 minutes left in the third.
Then, in 2:26 apart, the Hurricanes put on the best pressure of the night, and it paid dividends.
Mark Jankowski, off the fourth line, scored his very first goal this postseason to tie things up 2-2.
William Carrier and Eric Robinson both recorded their fourth assists of the playoffs.
With exactly five minutes left to go, the Canes went on their third power play of the game. And to everyone's surprise, their rough power play unit would pull through to continue the rally.
Jordan Staal scored his fourth goal of the playoffs to make it 3-2, not even a full minute into the power play.
Vegas would have a power play chance of their own with 3:28 left to go. But they would only put up one shot on goal, making it their only one of the night on their four power play chances.
It marked 56 out of 60 successful penalty kills by the Hurricanes these playoffs.
However, Vegas would find the net with just a little over a minute left as Mark Stone scored his sixth of the postseason.
Marner recorded his second assist of the game, surpassing Ovechkin for the second-most points (17) in a player's first 10 road playoff games for one franchise.
Tomas Hertl, who assisted on Stone's game-tying goal, picked up a tripping penalty in overtime, and it proved costly as it was Carolina who proved victorious behind Jarvis' goal as the series now heads to Las Vegas for Game 3 on Saturday, June 6th.