The Canadiens, who had made the playoffs in each of the last four years, finished the season in last place in the Eastern Conference.
Tomas Plekanec and Max Paciorietty gave Montreal a 2-0 lead through two periods and Budaj kept the Canadiens in front.
Dion Phaneuf spoiled Budaj's shutout bid just 25 seconds into the third, but Erik Cole and Brad Staubitz added insurance goals for Montreal. It was the first and only goal of the season for Staubitz, who logged more than 100 penalty minutes during the campaign.
Ben Scrivens gave up three goals on 25 shots for Toronto, which has missed the playoffs eight years in a row.
Notable deaths of 2014 [PHOTOS]