Nazem Kadri and Tyler Bozak scored for the Maple Leafs, who are coming off a seventh straight year of missing the playoffs.
The lengthy period of futility resulted in the firing of General Manager Brian Burke last week. He was replaced with former Vancouver GM Dave Nonis.
He was brought in to take over for interim mentor Randy Cunneyworth after the Habs finished in last place in the Eastern Conference in 2011-12.
Montreal goalie Carey Price made 24 saves.
Notable deaths of 2014 [PHOTOS]