The Canadiens have not lost to Phoenix in 13 seasons.
Montreal's regulation goals came in the second period from Brian Gionta and Travis Moen, giving the Canadiens a 2-1 lead going into the third. Raffi Torres tied it on a wrist shot 5:50 into the final period.
Carey Price made 32 saves for Montreal, which had lost two in a row. Mike Smith gave up three goals on 36 shots.
The last win for the Coyotes over Montreal came Dec. 9, 1998. Thursday's game was their only scheduled meeting this season.
Celebrity Families of 2014 [PHOTOS]