
Tomas Tatar, Brendan Gallagher, and Joel Armia also scored for Montreal. Jonathan Drouin had a career-best four assists, defenseman Jordie Benn added two assists and Carey Price made 28 saves.
Tatar, a former Red Wing, opened the scoring 6:16 in. He fought off Detroit rookie defenseman Filip Hronek to get to a bouncing puck for a partial breakaway and beat Howard with a forehand shot for his 22nd goal.
The Canadiens added five goals in the second period.
Shaw scored the first (2:22) and last goal of the period (43 seconds left). Gallagher scored his 27th with 8:41 left, Domi scored with 6:12 remaining and Armia netted his seventh with 3:51 left.
Mantha spoiled Price's shutout bid with his 16th goal with 1:44 remaining in the middle period.
Domi got his second goal and 22nd of the season, and Shaw completed his hat trick in the third. Shaw has 16 goals this season.
NOTE: Drouin's assists were his first points in eight games. . Detroit D Trevor Daley was a late scratch with an upper-body injury. He was replaced by D Jonathan Ericsson. . The Canadiens lost 2-1 to the New Jersey Devils on Monday night. . Red Wings RW Thomas Vanek did not play because of a hip flexor injury.
UP NEXT:
Montreal: At New York Rangers on Friday.
Detroit: At Arizona on Saturday.