Jesperi Kotkaniemi and Phillip Danault also scored for the Canadiens, who improved to 7-1-1 in their last nine games. Jonathan Drouin had three assists.
Anaheim has allowed 19 goals in the past three games, including a 9-3 loss in Winnipeg on Saturday and a 6-1 defeat in Toronto on Monday.
The Canadiens were all over the Ducks from the opening faceoff, scoring twice before the visitors even got their second shot on goal.
Gallagher got the first at 7:11 of the first period after a sustained forecheck by Danault led to a turnover by Josh Manson.