Lecavalier gave the Lightning a 2-0 lead at 2:23 of the second when he put his stick between his legs and sent a shot past Montreal goalie Carey Price.
Niittymaki recorded his first shutout of the season and fifth overall. He made a glove save during a first-period breakaway by Montreal left wing Benoit Pouliot.
Martin St. Louis and Steven Stamkos also scored for Tampa Bay, which has its first three-game winning streak since beating the Canadiens on Jan. 27, 2009.
Montreal was coming off a 2-1 loss Tuesday night at Florida. Canadiens coach Jacques Martin remains tied for ninth place on the career NHL coaching victory list (542) with Billy Reay.
St. Louis put the Lightning up 1-0 from the low slot off a pass from Steve Downie at 9:50 of the first.
After Lecavalier scored early in the second, Stamkos made it 3-0 on his 28th goal this season from the left circle during a power play with 14:06 left in the period.
Montreal left wing Michael Cammalleri had his five-game points streak (five goals, eight points) end.
The teams were sent to their locker rooms with 1:38 left in the second to allow for the repair of a broken pane of glass. After a normal between periods break, the third period was started immediately after the remaining time in second was played.
NOTES: Stamkos has a goal in three straight games. ... Montreal D Jaroslav Spacek didn't play due to the flu. ... Lightning G Mike Smith returned as the backup after missing the previous six games because of a strained neck. ... Montreal D Paul Mara (upper body) missed his third straight game.