"It seems like a lot of those guys, they just try and drag you across the net and look for an opening," Price said. "It's pretty smart, but if you don't find an opening, it's not as good."
After Simon Gagne scored on Tampa Bay's third attempt to extend the shootout, Cammalleri snapped a shot past Dwayne Roloson. Price then waited out Teddy Purcell's deke for a glove save to secure the win.
Price stopped 35 shots, and Brian Gionta and Andrei Kostitsyn had goals in regulation for sixth-place Montreal, which has 85 points -- three fewer than fifth-place Tampa Bay in the Eastern Conference playoff race.
"It starts with your goaltender. Carey was strong," Canadiens coach Jacques Martin said. "It was a big win with all the injuries we have. We played well 5 on 5. Their two goals were on the power play and they have a good one, but we did well at even strength."
The Lightning, who are looking to make the postseason for the first time since 2007, have two wins in nine games (2-4-3).
"We're still fighting," said Tampa Bay coach Guy Boucher, who coached Montreal's AHL affiliate in Hamilton last season. "If you would have told us [last] summer that we would be fighting with teams like Washington, Boston and Philadelphia at this time of the year, I don't think anybody would have believed us."
Roloson, who made 26 saves, dropped to the ice after he was stung in the mask by Scott Gomez's slap shot 42 seconds into overtime. He remained in the game after being checked out by the trainer.
Gagne scored his 12th goal on a power play 9:29 into the third to tie it at 2. Purcell also scored with the man advantage early in the second.
"I don't know what happened there and certainly Vinny is not the type to lose his cool for nothing," Boucher said. "I'm anxious to see what happened."
Stamkos, who leads the league with 43 goals, nearly added to his total shortly after Kostitsyn tied it at 1. The Lightning center took a pass from St. Louis and drove to the net. Thinking that he had crammed the puck past Price, he raised his stick briefly before referee Steve Kozari waved his arms. A video review confirmed that the puck hadn't crossed the goal line.
Gionta gave the Canadiens a 2-1 lead earlier in the period with his 25th goal.
Gionta took the puck from St. Louis near the Montreal blue line and raced down the ice on a breakaway. The Canadiens captain went to his backhand and flipped the puck past Roloson for an unassisted goal, his second short-handed tally this season.
St. Louis, who assisted on Purcell's goal early in the second, set up Gagne's tying goal on another power play midway through the third.
Lecavalier and Subban engaged in a heated battle for position in front of the Canadiens' net while the Lightning were on a power play late in the first. Slashed by the Montreal rookie as he carried the puck out from behind the net, Lecavalier swung his stick sharply in retaliation, striking Subban in the midsection.
Tampa Bay began the second period with a 4-on-3 power play. Purcell took advantage of the extra space and scored his 17th goal 35 seconds in.
Kostitsyn took a fine pass from David Desharnais and got the Canadiens even at 1 with his 18th goal at 5:40.
Aaron Palushaj played his first NHL game and Nigel Dawes made his Montreal debut. Both were recalled from Hamilton of the AHL on Wednesday after Tomas Plekanec and Jeff Halpern sustained lower body injuries on Tuesday.
Canadiens coach Jacques Martin said neither of the injured players would travel with the team for Friday night's game in New York against the Rangers.
Boucher said Gagne is doubtful for the Lightning's next few games. "He's got some procedure we might have to do," Boucher said. ... Canadiens D Roman Hamrlik played his 1,300th regular-season game. ... Montreal D Hal Gill was ill and didn't play. He will travel to New York and be a game-time decision.