Paul Byron scored twice for Montreal (14-10-5), which won 5-2 at Bell Centre on Tuesday.
"What I wanted from the guys is that we were willing to play both kind of games," Canadiens coach Claude Julien said. "Play solid, play strong, not crack, just hang in there and we'd eventually get our chances. I thought the guys did a good job of that."
WATCH: [All Canadiens vs. Senators highlights]
Carey Price made 19 saves for the Canadiens, who are 3-1-0 in their past four games after a five-game losing streak.
Mark Stone and Colin White scored, and Craig Anderson made 38 saves for Ottawa (12-14-3), which had won three in a row before playing Montreal.
"Anytime we lose to Montreal, it stings a little bit more," White said. "We made a couple mistakes and it cost us again."
The Canadiens outshot the Senators 43-21, and 84-51 in the two games.
"We've talked about how we want to finish," Julien said. "Especially when you have the lead, it's easy to kind of sit back and get comfortable, and we've done that at times this year. That's an area we're trying to improve on. I think in the last little while we've been better in the third and we've kind of controlled the period, even though we've been in the lead."
Stone's wrist shot got through traffic to give the Senators a 1-0 lead at 7:58 of the first period. Jeff Petry's wrist shot from the right point tied it 1-1 at 8:18.