Montoya notched a second victory in two starts for the Jets, who racked up a fourth victory in five games.
Winnipeg broke a 1-1 tie early in the third period when Price was caught out of the net trying to play the puck. Andrew Ladd got control and quickly passed to Frolik, who scored before Price could get back into position.
Tobias Enstrom also scored for Jets.
Brian Gionta supplied the only goal for the Canadiens, who dropped a second straight.
Price finished with 31 saves.
Notable deaths of 2014 [PHOTOS]