Brendan Gallagher scored the go-ahead goal for Montreal -- his seventh of the season -- at 12:03 of the third period. The score capped a comeback which saw the Canadiens fire 13 shots on net in the final 20 minutes to only two for the Lightning, who went 18:16 of the third period without a shot.
"Going into the third we just talked about going in there and getting traffic to the net and making it tough on the goaltender," Gallagher said. "I thought we did a good job of it and on that goal [Max] Pacioretty battled behind the net, got the puck out front and I was lucky enough to jam it in."
Montreal cut the Lightning lead to one just 3:40 into the third, when Brian Gionta was credited with his eighth goal of the season via the power play, as the puck trickled into the net just one second before Victor Hedman's tripping penalty was set to expire.
Cedrick Desjardins, making his first start in goal for Tampa Bay since Jan 1, 2011 when he defeated the New York Rangers 2-1, had made the initial save, but he lost track of the puck as it caromed around several sets of legs in the crease before slipping behind him.
"The puck was under me for a while, but I guess it wasn't covered," Desjardins said. "I wasn't moving because I didn't want to put the puck in. They [Canadiens] battle hard. You could tell in the third, they wanted to win that game."
That score opened the floodgates as the Canadiens surged in the final period.
"This is what good teams are supposed to do," Montreal coach Michel Therrien said. "That showed a lot of character from the players, coming back and finding a way to win this hockey game."
The Canadiens (16-5-4) knotted the score 3-3 at 7:33 when Alexei Emelin's shot from the left point deflected off Lightning forward Alex Killorn and beat Desjardins. The goal was Emelin's second of the season and was assisted by Gionta and Michael Ryder.
"I had a good look at it but I was going the opposite way," Desjardins said. "It happens. A deflection and you don't have, like, three seconds to think. You hope your positioning is great, but unfortunately my positioning wasn't the best on that play."
After a scoreless first period, the Lightning took their time getting under way in the second, but once they got started, they were effective, peppering Montreal goaltender Carey Price with 11 shots and scoring three times.
Tampa Bay went without a shot on net until 5:30 into the second period, but made its first one count as Steven Stamkos, alone in the high slot, unwound on Martin St. Louis' centering pass and beat Price high to the glove side. It was the 19th goal of the season for Stamkos, tops in the National Hockey League.
The Lightning grabbed the lead back just 37 seconds later on Sami Salo's second goal of the season, a shot from just above the faceoff circle to the left of Price, who didn't appear to see it.
The combined three-goal barrage came in a 2:45 span, but Tampa Bay wasn't finished yet. With Plekanac in the penalty box for tripping, St. Louis sent a shot on net from just inside the blue line that deflected off Ryan Malone's foot and into the Montreal net to make it 3-1. The power-play goal at 12:20 was Malone's fifth of the season and was the second assist in the game for St. Louis. Stamkos also picked up his second point with the additional assist.
With two points in the contest, St. Louis extended his point streak to six games.
"I felt at 3-1 we were playing very solid hockey," Lightning coach Guy Boucher said. "Our power play worked. Our 5-on-5 forecheck worked. Our defensive zone was terrific."
But it didn't last and the Lightning (10-14-1) dropped their fourth consecutive game at home after starting the season with five consecutive home-ice wins.
"We're not hungry to win; we're scared to lose right now," Stamkos said. "The first two or three minutes of the third period, instead of keeping the pressure on them we were dumping the pucks in to nobody, just giving the puck right back to them. The game is about puck possession and we're giving the puck right back to them. Then they get a power play, break out of their zone and score. They got the momentum now and it's a different game.
"When you're in these situations things creep into your head when you're not winning games and you're finding ways to lose. It's natural. You have to find a way not to have that. We have to have the mentality of being hungry to win. A good team, a 3-1 lead at home, going into the third, that should almost be automatic. Right now, it's clearly not."
Price finished with 20 saves for his 13th win of the season.