It was the Lightning's first victory since Nov. 21 against Nashville.
Olaf Kolzig stopped 31 shots and was perfect over the final two periods.
Montreal's lone goal came on the power play from Patrice Brisebois to open the scoring 5:34 into the contest. St. Louis tied the game midway through the first and then he produced the contest's last score shorthanded 8:31 into the second.
Montreal had won four of its previous five. Jaroslav Halak made 19 saves in the loss.
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