Joel Armia had a goal and an assist, scoring on a breakaway on a power play seven seconds into the third period, and Carey Price made 29 saves for Montreal (5-4-2), which had lost consecutive games.
"You don't get too many chances to get breakaways in this league, so I want to make sure I bury those when I get a chance," Drouin said. "And I was happy to bury two, and lucky to get two breakaways."
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Jake Muzzin and Andreas Johnsson scored, and Michael Hutchinson made 33 saves for Toronto (6-5-2), which lost the second of back-to-back games.
The Maple Leafs, with Frederik Andersen in goal, defeated the San Jose Sharks 4-1 on Friday.
"I didn't think we were competitive enough in the first period," Maple Leafs coach Mike Babcock said. "I thought we were really competitive and got the game going in the second, and then we gave them three goals in the third, any way you look at it. We made mistakes and they just shot it in the net, so we gifted them those three. It's disappointing because we had crawled our way back and kind of set the tone."
Armia gave Montreal its second lead at 3-2 when he stripped the puck from Muzzin after the opening face-off before driving in alone to score his sixth goal on a shot inside the right post.
"Obviously when you get chances and you put the puck in or create chances all the time it's going to bring your confidence up," Armia said. "And I'd say it's pretty much easier to play with a lot of confidence than without any."
Drouin, who scored on a breakaway in the first, made it 4-2 at 7:40 when he broke in alone again and scored unassisted.