"This losing streak is not easy on anybody," Montreal coach Randy Cunneyworth said. "The one thing you have to do is have a little pride and you have to keep working hard."
The Panthers scored twice in the first four minutes of the second to take a 3-2 lead.
Florida opened the second on the power play. Bergenheim took a shot from low in the left circle that beat Budaj and made it 2-all.
Weiss got his second goal when he grabbed a rebound in front and poked in the puck at 4:01 to give the Panthers a 3-2 lead.
"It was nice to get a couple bounces," Weiss said.
The Panthers overcame a two-goal deficit for the second consecutive night. The Panthers trailed Carolina 2-0 before winning 3-2 in a shootout Saturday night.
"We proved last night that we can come back and win it," Clemmensen said. "It is fresh in our minds and we were able to put it together again tonight. It was a big two points."
Campbell scored on a slap shot from the high slot at 9:52 of the third to make the score 4-2.
"They came at us in waves early. Give Montreal credit, they played an extremely hard game," Panthers coach Kevin Dineen said. "We had an answer for it tonight, which was nice."
Trailing 2-0, the Panthers closed to 2-1 on Weiss's first goal. Weiss took a pass from Keaton Ellerby in the slot, turned and wristed the puck past Budaj at 11:36 of the first. It was Weiss's first goal in 12 games.
"It was a big goal just to give us a little life, being down two," Weiss said.
Montreal took a 1-0 lead 4:27 in, when Erik Cole took a shot that was blocked and Desharnais wristed the rebound past Clemmensen.
The Canadiens stretched their lead to 2-0 on Subban's power-play goal with a two-man advantage. Subban took the puck in the left circle, moved it to the slot, and fired a shot that went over Clemmensen's shoulder at 6:55.
The Canadiens only took four shots in the second period.
"We're getting chances, but we can't seem to get over the hurdle," Desharnais said. "It isn't for lack of effort, we just have to find a way to push through this. It's not a position we want to be in by any means. We're fighting ourselves mentally right now."
Florida LW Wojtek Wolski, acquired from the Rangers on Saturday, and RW Jerred Smithson, acquired from Nashville on Friday, both made their home ice debuts ... Budaj made his ninth appearance in goal for Montreal.
Copyright by STATS LLC and The Associated Press
Arena: BB&T Center Location: Sunrise, Florida
Referees: Gord Dwyer, Chris Rooney Linesmen: Darren Gibbs, Jonny Murray
Attendance: 18,108 (94.1% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
David Desharnais (12)
Assist: Erik Cole
P.K. Subban (4)
(Power Play) Assists: Tomas Kaberle, David Desharnais
Stephen Weiss (14)
Assist: Keaton Ellerby
Sean Bergenheim (14)
(Power Play) Assists: Mikael Samuelsson, Scott Clemmensen
Stephen Weiss (15)
Assists: Mikael Samuelsson, Sean Bergenheim
Brian Campbell (4)
Assists: Stephen Weiss, Sean Bergenheim