Reimer made 37 appearances last season and recorded a 2.60 goals-against average. He began his second campaign in outstanding form, turning aside 14 shots in the final period to get the win.
He had three shutouts during his rookie campaign.
The game was scoreless until Matthew Lombardi put a wrist shot past Carey Price 33 seconds into the middle period with the Maple Leafs shorthanded.
Dion Phaneuf scored on a slapshot with 4:41 having expired in the third.
Price stopped only 16 shots.
Montreal reached the playoffs last year, but was eliminated in seven games by eventual Stanley Cup champion Boston in the first round. The Maple Leafs failed to make the playoffs.