The Senators reached 84 points for the season, moving them past idle Boston in the battle for the division lead.
Kuba beat Carey Price with a wrist shot after taking a feed from Daniel Alfredsson. Ottawa faced a 1-0 deficit until Colin Greening scored on a backhander 6:27 into the third period.
The win went to Ben Bishop, who had to make only 13 saves. Bishop did not allow a goal after giving up a shorthanded tally to Tomas Plekanec 8:18 into the contest.
Price stopped 31 shots. Montreal has won three of the five meetings with the Senators this season.