Austin Czarnik and Raymond scored, and Husso made 31 saves for Detroit (7-3-3), which won its previous three.
"We got looks on the power play and we built momentum," said Larkin, the Red Wings captain. "We kept them hemmed in their end and wore them out, so they kept taking penalties. You'd like to see one go in, but some nights it doesn't go in."
With the game tied 2-2 and 5:32 left in the third period, Canadiens forward Juraj Slafkovsky was given a major penalty and game misconduct for boarding Red Wings forward Matt Luff, who left the game.
Detroit coach Derek Lalonde said Luff sustained a significant injury on the play and that he'll probably be out a similar amount of time as Filip Zadina, who is sidelined 6-8 weeks with a lower-body injury.
"We don't know his exact status," Lalonde said. "We'll know more tomorrow, but he's not going to be on the ice for quite a while. As for the play, the right call was made. That's the exact play we try to avoid, and that's why -- a player got seriously injured."
Detroit had two shots in the first 1:58 of the penalty before Elmer Soderblom was called for interference to make it 4-on-4. Neither team scored, and Montreal was able to kill the rest of Slafkovsky's penalty.
"It is always going to be tough to kill a five-minute power play, but the situation is even tougher when there is only five minutes and change left in the game," St. Louis said. "Luckily, we won a couple draws, got a couple clears and then drew the penalty that let us cut the kill in half."
Larkin hit the crossbar 32 seconds into overtime, and Husso stopped Hoffman from point-blank range at 1:09.
Hoffman gave Montreal a 1-0 lead at 5:41 of the first period, knocking in the rebound of Gallagher's shot.