''We stuck with it,'' said Stamkos, who had seven shots. ''I thought we got better as the game went on.''
Brendan Gallagher scored and Price stopped 31 shots for Montreal, which has lost seven of 10.
''Obviously we're very disappointed with the result but for the most part I thought we played well,'' Price said.
Nikita Kucherov negated a potential icing by getting past Canadiens defenseman Karl Alzner and sent a backhand pass from behind the net to Stamkos, who tied it at 1 with 12 seconds left in the second.
''I didn't say a word,'' Stamkos said. ''I knew that he knew that I was there.''
''An awareness play,'' Tampa Bay coach Jon Cooper added.
Kucherov has seven assists and 12 points during an eight-game point streak.
Point put the Lightning up 2-1 during a goalmouth scramble 30 seconds into the third.
Stamkos' 15th goal made it 3-1 on a 5-on-3 power play 4:45 into the final period.
Gallagher opened the scoring early in second when the puck went off his glove during a power play.
Tampa Bay's NHL-best power play went 1 for 6. Montreal converted one of its three man-advantage chances.
Canadiens center Jonathan Drouin was held off the scoresheet in his first game against former team. Taken third overall in the 2013 draft by Tampa Bay, Drouin was traded to Montreal in June for defenseman Mikhail Sergachev.
''It's frustrating,'' Drouin said. ''The offensive players are supposed to produce a number to help the team win and we haven't done that in a while. It's not like we're missing chances, we just aren't getting many chances and that's frustrating.''
NOTES: Tampa Bay D Anton Stralman, who entered as the NHL leader at plus-24 this season, sat out with a lower-body injury. ... Montreal LW Max Pacioretty became the ninth player from the 2007 draft to play in 600 NHL games. ... Tampa Bay RW Ryan Callahan (upper body) resumed practicing in a no-contact jersey. ... Price, 281-187-57 overall, is 12-13-6 against the Lightning.
Canadiens: Play at Florida on Saturday night.
Lightning: Host Philadelphia on Friday night.
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