Belfour is now tied with Tony Esposito for eighth on the all-time shutout list. Jay Bouwmeester scored the winner for the Panthers (22-25-11), who won their second in a row after a three-game losing skid.
Cristobal Huet made 24 saves but still took his fourth straight loss for the Canadiens (29-23-6), who allowed the game's first goal for the ninth straight game and saw their record drop over that span to 2-6-1.
Montreal's loss coupled with a 2-1 win by the Carolina Hurricanes dropped the Canadiens to eighth place in the Eastern Conference standings.
The Canadiens dropped to 1-3-0 against the Panthers this season in the final game between the two clubs, with Montreal scoring only twice in regulation in the four games.
The Canadiens were playing without winger Alex Kovalev, who went to the hospital after practice Monday to have some tests done on an undisclosed "upper body injury" and didn't take part in the morning skate on Tuesday.
Kovalev was benched for nearly the entire third period in Saturday's 5-3 loss to the Ottawa Senators after his turnover eventually led to the game-winning goal 17 seconds into the final frame. Sergei Samsonov took Kovalev's spot on the first line with Saku Koivu and Chris Higgins, marking the first time this season Samsonov has started a game on Koivu's line.
After a first period with few scoring chances to speak of - aside from partial breakaways by Higgins and Drew Larman seconds apart about seven minutes in - the Panthers took a 1-0 lead late in the second.
Olli Jokinen sent the puck in front from behind the net, a scramble ensued and the puck popped out to Bouwmeester, who banked it in for the defenceman's ninth of the season at 16:16.
Montreal left the ice at the end of the second to a stream of boos from the sellout Bell Centre crowd of 21,273.
The Panthers appeared to take a 2-0 lead at 10:49 of the third when Kamil Kreps shot the puck into an empty net, but the goal was waved off by referee Kerry Fraser because Juraj Kolnik had accidentally knocked Huet to the ice.
Montreal had a glorious opportunity to tie the game when Alexei Semenov and Stephen Weiss took penalties six seconds apart with just under six minutes to play in regulation, but the Canadiens managed just three shots before Koivu took a tripping penalty late in the two-man advantage. Then with the Montreal net empty and 28 seconds to play in regulation, Higgins hit the post after a series of saves by Belfour.
Notes: The Canadiens were also without winger Mike Johnson (flu), while defenceman Craig Rivet missed his third game with pneumonia. Defenceman Janne Niinimaa was a healthy scratch . . . In the absence of Rivet and Kovalev, Steve Begin wore an "A" as alternate captain . . . The Panthers were missing C Jozef Stumpel (shoulder), winger Rostislav Olesz (shoulder) and defenceman Branislav Mezei (shoulder). Centre Gregory Campbell was the lone healthy scratch . . . Panthers D Alexei Semenov, who left to play in Russia earlier this season and was suspended by the club as a result, was called up from the minors on Monday and made his season debut Tuesday against Montreal.