But then they got goal off a fortunate bounce, veteran goalie Roberto Luongo made some key saves and the Panthers pulled out a 3-2 victory on Thursday night.
"We've been doing that all year," said Luongo. "We never quit.
"No matter what the score is, we believe in our chances to win the game. There was no panic and we got the job done."
The Canadiens (37-16-5) took the lead on a pair of goals from Brendan Gallagher, but Tomas Fleischmann got one back and recent call-up Steven Kampfer scored his first NHL goal since 2012 to tie it 4:57 into the third period and force overtime.
Dave Bolland got the game-winner in the sixth round of a shootout for Florida (26-19-12), which has won the first two games of a five-game road trip that takes them to Ottawa on Saturday.
The win puts them only one point back of Boston for the eighth and final Eastern Conference playoff position.
"We don't want to get ahead of ourselves," said Luongo. "We realize we're in the thick of things, which is exciting and fun for our group but we have to take it a game at a time."
The Canadiens, dealing with injury trouble for the first time this season, still outshot Florida 39-21.
Montreal used five players who were on its AHL club in Hamilton earlier this season— defencemen Nathan Beaulieu, Greg Pateryn and Jarred Tinordi and forwards Christian Thomas, Jacob de la Rose, as well as rookie Jiri Sekac.
"We're a young team, but our team worked extremely hard," said coach Michel Therrien. "I liked the effort."
Gallagher was in his usual spot, in front of the opponent's goal, when he banged Max Pacioretty's rebound past Luongo 2:31 into the second period. He was there again to put in a loose puck at 10:32. Gallagher got his 100th career point along the way.
Only 1:22 later, the Panthers got two chances from the slot and Fleischmann buried the second on a rebound off Andrei Markov's skate with Bolland parked in front of Carey Price.
A Florida power play had just ended when Fleischmann set up Kampfer for a quick shot that beat Price on the short side at 4:57 of the third. It was Kampfer's first NHL goal since 2012 when he was with Minnesota.
"I just saw right over his pad and I was lucky to get it over him," said Kampfer. "It was huge to get that goal and get us back in the game.
"It's definitely a huge win for us, for the standings and for morale on this team."
It was a second game in a row in which Montreal outshot an opponent but lost the game. They had a 44-39 advantage Wednesday night in a 4-2 loss in Ottawa.
"We had enough chances, but (Luongo) is a good goalie and he made some pretty good saves," said Gallagher. "But, at the same time, there's always ways to beat goalies and we have to find a way to do that."
Notes — Montreal's Alex Galchenyuk was out with a flu. . . Defenceman Alexei Emelin, injured Wednesday in Ottawa, will miss at least a week, then be re-evaluated . . . Rearguard Sergei Gonchar was placed on injured reserve. . . Jarred Tinordi was recalled from AHL Hamilton. . . It was a fourth straight Montreal home game to go to OT. . . Florida's Dmitry Kulikov sat out the third of his four-game suspension.