With the goal, Domi extended his scoring streak to six games. The last Habs player to enjoy a six-game goal-scoring run was Max Pacioretty, back in January 2015.
The teams headed to the room tied at 1-1 after 20 minutes.
Carolina took the lead again with 12:26 to go in the middle frame when Erik Haula beat Charlie Lindgren to make it 2-1.
Rod Brind'Amour's squad was leading 22-19 in shots after 40 minutes.
There was some bad news for Habs fans, as Gallagher left the game in the second period after a run-in with teammate Ben Chiarot. He did not return.
Lindgren made an incredible save early in the third period to keep his team in the game.