Rinne made 20 saves in the game and faced only six shots on goal in the second period.
Nashville outshot the Habs 55-20, including a 23-shot onslaught in the opening period against Montreal goalie Carey Price.
Steve Sullivan scored both Nashville goals. He beat Price at 10:48 of the first period and added a power-play goal at 12:59 of the third.
The win was Nashville's fourth in its last six games.