After 40, the Canadiens were leading 3-2 in the score and 26-23 in shots.
In the third, with a delayed penalty, rookie Cale Fleury - making his NHL debut - accepted a pass and broke away. He put the moves on Mrazek, but the Czech netminder denied him his first career goal in the big leagues.
Erik Haula tied things up with 13:05 left in regulation.
With that, the game would need extra time to come to a decision and despite some sustained pressure by the Canadiens in the Hurricanes' end, the game was still tied after overtime.
In the shootout, Dougie Hamilton scored the lone goal for Carolina, while neither Paul Byron, Jonathan Drouin, nor Nick Suzuki could solve Mrazek.