Carey Price made 11 saves in his first game since April 5 for Montreal (19-14-9), which was 2-4-0 while he was out with a lower-body injury.
"I felt pretty good," Price said. "You know, whenever you take a break there's always a bit of an adjustment period getting back, but I thought the adjustment was pretty quick."
Jake Allen made six straight starts when Price was injured, including a 2-1 win against the Calgary Flames on Friday.
The Canadiens are fourth in the seven-team Scotia North Division, six points ahead of the Flames. The top four teams will qualify for the Stanley Cup Playoffs.
"We just need to find some consistency," Price said. "I think everybody in the League wants to find that. You know everybody in this league wants to win and everybody's playing hard, so we just have to find that on a nightly basis."
It was the Senators' first shutout under coach D.J. Smith and first since March 26, 2019, when Craig Anderson made 35 saves in a 4-0 win against the Buffalo Sabres. Anderson was also in goal for Ottawa's last shutout on the road, making 25 saves in a 6-0 win at the Flames on Oct. 13, 2017.
"Our execution wasn't good at times, and we didn't get enough traffic in front of [Murray]," Canadiens coach Dominique Ducharme said.