Domi extended his goal-scoring streak to four games with the tally, and his points streak now runs at five games.
For his part, rookie Nick Suzuki earned a helper on Domi's goal, making it a fourth straight game in which he's earned a point.
The Lightning halved the Habs' lead with 59 seconds remaining in the first thanks to Alex Killorn.
The Canadiens dominated the first half of the period, with Tampa only getting its first shot on goal with 7:35 left in the stanza.
Montreal led 20-10 in shots after 20 minutes.
Steven Stamkos made it even just 1:34 into the second when he picked up his own rebound and beat Carey Price to make it a 2-2 game.
The Lightning got their first lead of the night a few minutes after the Stamkos goal when Mitchell Stephens potted his first in the NHL.
Killorn netted his second of the game with eight minutes left in the middle frame two double the lead for the hosts.
The Canadiens would reduce that lead just 13 seconds later.
Defenseman Ben Chiarot jumped on a Brendan Gallagher rebound to make it 4-3. The goal tied Chiarot's career high in a season with five.