Montreal, which entered 3-1 in the playoffs when scoring the opening goal and 1-5 when it does not, struck first on Niklas Sundstrom's even-strength goal at 5:46.
After Lightning defenseman Dan Boyle lost the edge of his skate in the Tampa Bay zone, Joe Juneau fed Sundstrom skating down the slot, and Sundstrom scored on a backhand shot from the lower-right circle.
The Lightning had a chance to even the score when Andrei Markov was whistled for high sticking at 7:24. But the Lightning managed only one shot on goal while allowing a couple of odd-man breaks.
Tampa Bay failed to take advantage of a second man-advantage opportunity after Alex Kovalev was penalized for goaltender interference at 14:19.
THE POSITIVE: Lightning defenseman Pavel Kubina hustled back to make a sliding stick check to break up Steve Begin's breakaway opportunity with five minutes remaining.
THE NEGATIVE: Fredrik Modin was penalized for holding at 19:03, giving Montreal a power play that carried into the second period.
KEY PLAY: Montreal's Jose Theodore made a pad save on Darryl Sydor's shot from the left circle after Michael Ryder pinched from the left point, freeing Sydor and Kubina for a two-on-one.
KEY PLAYER: Knowing he would have to outplay Nikolai Khabibulin to extend the series, Theodore stopped every shot he faced, including Dave Andreychuk's stuff attempt from in front during a Tampa Bay power play.
Period two: Boyle, Richards score
Each team started the period short-handed. The Lightning had to kill the final 1:04 of Fredrik Modin's holding penalty, and Montreal was without wing Richard Zednik, who suffered a high ankle sprain in the first.
The Lightning tied it on Dan Boyle's power-play goal at 11:57. With Michael Komisarek off for unsportsmanlike conduct, Vinny Lecavalier's pass from behind the Montreal net deflected off Boyle's skate and past Jose Theodore.
Brad Richards gave Tampa Bay its first lead with an even-strength goal with 2:46 left. With Montreal caught in a line change, Richards intercepted Jim Dowd's backward pass and beat Theodore with a backhander over the shoulder after a give-and-go with Dmitry Afanasenkov.
THE POSITIVE: After being outplayed and outshot in the first period, the Lightning maintained its composure and regained control of the game with a pair of goals.
THE NEGATIVE: The Lightning failed to capitalize on four power-play opportunities before Boyle converted.
KEY PLAY: Sheldon Souray's shot from the top of the left circle at 11:26 got through Nikolai Khabibulin's legs but hit the left post before Khabibulin covered the puck.
KEY PLAYER: For the second straight game, a Richards goal put the Lightning ahead.
Period three: Defense takes priority
With Montreal needing a goal to extend its season, the Lightning played smartly. Tampa Bay made it difficult for the Canadiens to move through the neutral zone and kept the majority of shots from getting to Nikolai Khabibulin.
Montreal got a power play when Dan Boyle was penalized for cross-checking at 12:03. One of the Canadiens' best scoring chances came when Patrice Brisebois' shot from the high slot missed wide and the puck caromed off the end boards toward the net. But Khabibulin quickly covered the puck.
Saku Koivu had an even better chance with 3:36 left, but Khabibulin smothered the captain's shot from the lower-right circle with his glove.
Fredrik Modin clinched the victory with an empty-net goal with 55.3 seconds remaining.
THE POSITIVE: For the second straight series, the Lightning closed out an opponent in its first opportunity.
THE NEGATIVE: By sweeping the series, Tampa Bay potentially faces a long layoff before the start of the conference final.
KEY PLAY: Montreal coach Claude Julien pulled goalie Jose Theodore with a little more than a minute remaining, setting up Modin's empty-netter.
KEY PLAYER: Khabibulin, who had never won a playoff series before last season, won his second of the season and third in two.
