Shore had no goals in the first 19 games this season, but scored for the second straight game to tie it 1-all at 18:22 of the second.
Spezza, who also has scored in consecutive games after netting only one goal in the first 19, put in a rebound just less than a minute later.
Shore had an assist on Spezza’s goal. So did Tyler Seguin, who scored into an empty net with 27 seconds to play.
Ben Bishop made 29 saves for Dallas on his 31st birthday. He allowed only a power-play goal by Brendan Gallagher at 12:04 of the second.
Gallagher scored on a rebound after Charles Hudon sent a slap shot from the blue line.
After that, the Stars killed off all three Montreal power plays in the third period.
Canadiens goalie Charlie Lindgren had 26 saves.
The Habs are in Nashville Wednesday night to face P.K. Subban and the Predators, puck drop is at 8:08 p.m.
— with files from the Associated Press