Montreal iced the game late in the third period when it went on the power play. Bergeron came in on Ottawa goalie Brian Elliott with the puck but was denied. Kostitsyn, however, put home the rebound with 2:12 left for a 3-1 Montreal lead.
Scott Gomez followed 67 seconds later with an empty-netter after stripping Ottawa defenseman Filip Kuba of the puck.
Michael Cammalleri got the other goal for Montreal, which won its third straight game. Tomas Plekanec picked up three assists. Jaroslav Halak stopped 15 shots in the crucial third period.
Mike Fisher picked up Ottawa's only goal while Elliott stopped 23-of-26 shots in the loss.