Brendan Gallagher and Jeff Petry scored power-play goals 2:04 apart in the second period, and Carey Price made 26 saves for Montreal (10-6-5), which had lost five straight (0-2-3) and is 1-1-1 since Ducharme replaced Claude Julien on Feb. 24.
"We're happy, obviously, not satisfied," Price said. "Definitely very happy for coach and [new assistant Alexandre Burrows]. You know, they've both been working really hard and I'm sure that they're pretty happy tonight and proud."
Canadiens captain Shea Weber presented the game puck to Ducharme after forward Jonathan Drouin, who was coached by Ducharme when he played for Halifax in the Quebec Major Junior Hockey League, picked it up off the ice before heading to the locker room.
"I don't know what I'm going to do with the puck, but one thing, it's going to have a special place for me," Ducharme said. "I mean to be having my first NHL win is special, and to have it with this team, with the Canadiens, is special for me, so it's going to have a special place.
"For [Drouin], he came in when he was only 16, it's like 10 years ago. And we've gone a long way together. We've won together in juniors (Memorial Cup champions in 2013), we've worked together since I'm here. I think there's respect on both sides. I didn't know he did that but it's a great gesture."