Tampa Bay was without Stamkos, its leading goal scorer, who broke his right leg after crashing into the net against the Bruins on Monday. Stamkos underwent surgery Tuesday afternoon and is expected to miss several weeks.
''(Tonight) was a big step in overcoming what we know is going to be a challenge for us,'' Lightning coach Jon Cooper said.
''It was obviously a tough loss whenever you lose a player like that,'' Bishop said. ''This is a team sport and we're going to move forward. The guys played great tonight. We could've easily won this game or we could've easily scored more goals.
''Carey Price played a great game, but we hung in there until the end and a big goal by Fil in the shootout.''
Daniel Briere scored for Montreal (9-8-2) and Carey Price made 44 saves.
''That was a big performance by Carey Price,'' coach Michel Therrien said. ''Carey gave us a chance to stick in the game.''
Malone put Tampa Bay on the scoreboard at 5:00 of the first when he deflected an Eric Brewer shot from the point.
Malone, who was shoved by Canadiens defenseman Douglas Murray seconds before Brewer's shot, deflected the puck while falling to the ice. The goal was his third of the season.
Montreal couldn't take advantage of three power-play opportunities in the first period. They finished the game 0 for 3 with the man advantage.
''We caught ourselves chasing, we weren't supporting the play, we weren't supporting the puck,'' Canadiens' Josh Gorges said. ''When you do that, you just end up skating all over the place.
''If you don't play with that extra grit, that intensity, jumping onto loose pucks, being first on pucks, that's what happens.''
Montreal captain Brian Gionta agreed: ''We had nothing, we didn't create anything.''
The Habs, who were outshot 13-5 in the second period, got a break when Radko Gudas beat Price with a shot from the point. The goal was disallowed when video replay suggested Tyler Johnson had obstructed Price on the play.
''We didn't compete hard enough to get success for two periods,'' Therrien said. ''To be able to score some goals, you have to compete. This is not what we did, honestly. We created some momentum in the third because we had some urgency, but I'm not impressed.''
Briere got the equalizer at 15:22 of the third when a Max Pacioretty shot went off his thigh and past Bishop.
''After the first two periods, Michel (Therrien) told us to go to the net a lot more,'' Briere said. ''There were a lot of shots where there was nobody in front of the net.
''On my goal, that's what I tried to do. I tried to go to the net. It was a good play by Pacioretty too to try to hit me like that.''
''My performance got better as the game went on,'' Briere said. ''In the first, I'll admit, I was a little nervous, a little disorganized. In the second, I was more comfortable. In the third, we got good scoring chances. I calmed down a little bit.''
Rookie J.T. Brown, who was recalled from Syracuse (AHL) after Stamkos' injury, recorded one shot in 14:37 of ice time. Brown played five NHL games with the Lightning in 2012.
Notes: The Canadiens have only won once in their past six games. They beat the New York Islanders 4-2 on Sunday. ... David Desharnais and George Parros were both healthy scratches. ... Defender Alexei Emelin, who has yet to play this season, is expected to dress over the weekend. Emelin underwent knee surgery last May.