Murray made 31 saves as Tim Stützle, Drake Batherson and Connor Brown had goals for Ottawa (17-26-4). Vancouver's (18-19-3) Thatcher Demko stopped 22 shots.
"Two power play goals in the first gets you the lead and then the penalty kill was good, the goaltending was exceptional," Sens head coach D.J. Smith said.
The Senators took a 1-0 lead 9:17 in as they scored on the power play for the sixth straight game as Stützle got the faintest of tips on Nicholas Paul's shot to score the eighth goal of his rookie campaign.
Batherson doubled the lead at 15:57 on the man advantage as Brady Tkachuk's pass hit Tyler Myers' skate and fell perfectly on the 22-year-old's stick on the edge of the blue paint as he elevated the puck for his 16th of the season.
It was the first time this season the Sens had scored two power play goals in the same period.
"It's always nice to score on the power play," Batherson said. "I think when you score two on the power play you've got a good shot at winning the game and that was the case tonight."
After a scoreless second, in which Ottawa killed two penalties and was outshot 12-7, the Sens iced the game with Brown's empty-netter with 90 seconds left in regulation as he scored his team-leading 17th goal of the season.
"Guys have done a great job of blocking shots, boxing out, letting me see the puck," Murray said. "It's unbelievable the team effort we've had the last few games."
The shutout was Murray's second in five days and the 13th of his NHL career. He turned aside all 23 shots he faced Saturday in Montreal.
"Murr made all the saves he had to, and then some," Smith said.
Paul's assist on Stützle was his 12th of the year, a new career high. With his goal acting as his 25th point of the year, Stützle became just the seventh Senator to hit that mark as a teenager after Alexandre Daigle (58 points), Tkachuk (45), Martin Havlat (42), Wade Redden (30), Radek Bonk (26) and Erik Karlsson (26).
The two teams meet again Saturday night at Rogers Arena as the Sens complete its four-game road trip.
