After Montreal pulled within one in the third on Alex Galchenyuk's power-play goal, Florida killed two penalties -- including 35 seconds of a 5-on-3.
"Our penalty killing came up big for us," Clemmensen said. "Our guys were diving in front, getting sticks up there, deflecting passes, being in a good position. It was great. That's how we win games."
The Canadiens have played 11 games in 19 days, including a 1-0 overtime victory over the Islanders in New York on Saturday night. The team touched down in Montreal in the wee hours Sunday, delayed by a snowstorm, and scratched their morning practice.
"We've played a lot of hockey in less than three weeks," Canadiens coach Michel Therrien said. "This team is drained. They're empty. The lemon is squeezed of all its juice.
"When physically, you're tired, the execution is not quite there, and you make bad decisions. They go hand in hand.
"I'm not blaming (the players). I see what we're asking of them. Very demanding. They're athletes, they're human beings. They gave what they could in the circumstances. I know what they could give, and they gave it."
Florida extended its winning streak to three games, and Montreal lost for the third time in four games.
"We had an opportunity to win the game, and we wanted to win the game," Montreal defenseman P.K. Subban said. "We have to capitalize on our opportunities."
Winchester opened the scoring at 4:44 of the second, beating Peter Budaj with a one-timer off the post. Tomas Kopecky started the play, drawing both Montreal defensemen behind the net before feeding Winchester.
Bjugstad scored at 7:11, finishing off a 3-on-2 rush by firing a wrister under Budaj's glove.
Galchenyuk scored at 2:28 of the third, banging home captain Brian Gionta's rebound from inside the crease.
The game was Montreal's third in four nights. ... The Panthers have won five of their last six games. ... Florida goalie Tim Thomas missed his second straight game after injuring his groin in practice Thursday. ... Budaj made his first home start of the season in place of Carey Price. ... Montreal has only scored three times in its last four games.