Mike Matheson had an empty-net goal and an assist, and Nick Suzuki also scored for the Canadiens (43-21-10), who have won seven of eight (7-1-0). Jakub Dobes made 36 saves.
Montreal pulled within two points of Tampa Bay for second place in the Atlantic Division, and remained four behind the Buffalo Sabres for first.
Jake Guentzel scored for the Lightning (46-22-6), who had their eight-game point streak end (6-0-2). Andrei Vasilevskiy made 19 saves.
Tampa Bay fell out of a tie for first place in the Atlantic, two points behind Buffalo.
Slafkovsky gave Montreal a 1-0 lead with a 5-on-3 power-play goal at 12:25 of the first period, a one-timer from the right circle off a pass from Ivan Demidov that beat Vasilevskiy five-hole.
Guentzel tied it 1-1 at 13:41 with a wraparound shot that got past Dobes short side after faking a shot on the far side.
Caufield put the Canadiens ahead 2-1 at 12:49 of the second period after Slafkovsky raced down the left side, drawing the attention of the defense, and sent a pass to the slot to Caufield, who scored on the tap into the open net.
Matheson scored into an empty net at 17:55 of the third period to make it 3-1 and Nick Suzuki added another empty-net goal at 18:54 for the 4-1 final.
