Tyler Johnson scored the go-ahead goal on a short-handed breakaway late in the third period, and the Lightning clinched a playoff berth with a 3-1 victory over the Canadiens on Tuesday night.
"Just being in the right spot and getting lucky sometimes," Johnson said.
The win and losses by New Jersey and Washington gave Tampa Bay its first postseason berth since 2011 and only its second in seven years. Montreal ended a five-game winning streak but also qualified for the postseason by virtue of the losses by New Jersey and Washington.
Canadiens goalie Carey Price took some consolation in advancing to the postseason.
"We're disappointed with our game today, but big picture, we've got to be happy with that," he said.
The win moved Tampa Bay, with a game in hand, into a second-place tie with Montreal in the Atlantic Division. The second- and third-place teams in each division will meet in the first round of the playoffs.
"It's just one game, but it's really the 76 games all bottled into one," Tampa Bay coach Jon Cooper said. "What you are really striving for is to win the Stanley Cup, but you cannot win the Cup if you don't get into the playoffs."
With teammate Nate Thompson serving a minor penalty for boarding, Johnson picked up a loose puck near the Montreal blue line, skated in on Price and backhanded a shot inside the left post with 7:19 remaining in the game.
Ryan Callahan made it 1-all on a power play 9:19 into the second, skating through the left circle toward Price and lifting a shot high into the net.
Tampa Bay was on a power play when Alex Killorn closed out the scoring with an empty-netter with 45 seconds left in the third period.
Bishop finished with 25 saves, while Price stopped 30 shots.
Tampa Bay winger Teddy Purcell slammed a shot past Price with 11.7 seconds left in the second period, but the officials ruled forward J.T. Brown made contact with the goaltender and disallowed the goal. The call drew an angry response from Tampa Bay fans after a replay appeared on the video screen.
The crowd also became irate when Montreal's Douglas Murray drew a match penalty for an illegal check to the head of fellow defenseman Mike Kostka, setting up a 5-on-3 advantage for the Lightning with 2:13 left in the game.
"If the crowd's reaction was anything after they saw it, then it seems that it was illegal," Cooper said. "Those are the hits you want to take out of the game. I'm sure Murray wasn't looking to hit him in the head."
Lightning forward Ondrej Palat, who earlier in the day was named the top NHL rookie for the second time in three months, assisted on the goals by Callahan and Killorn.
Tampa Bay C Valtteri Filppula, who came in with the longest points streak in the league at 12 games, came up empty. ... Montreal C Tomas Plekanec returned after missing one game for personal reasons. ... The home team won for the first time in the four-game season series. Lightning captain Steven Stamkos was sidelined with a broken leg for the first three games, each of which went to overtime tied at 1. ... Price came in victorious in nine of his 10 previous starts. Bishop improved to 8-1-1 in his past 10.