Murray, who's in his 11th season as Ducks general manager, took over as coach after firing Randy Carlyle on Sunday.
Jakob Silfverberg had the only goal for Anaheim (22-26-9), which was outscored 37-8 during its losing streak (0-7-0) and had not won at home since Dec. 12, a 6-3 victory against the Dallas Stars.
"I thought the emotion was good," Murray said. "I thought the effort was good. Some of the things we worked on in the last week, cleaning up our own zone a bit, were very good. Our defensive-zone coverage, our layers, the changes we made, I thought those were very good."
WATCH: [All Canucks vs. Ducks highlights | Anaheim welcomes 'Mighty Ducks' cast to drop puck]
Boyle was recalled from San Diego of the American Hockey League on Saturday, when the 26-year-old made his NHL debut in relief of Chad Johnson in a 6-2 loss at the Philadelphia Flyers. Starting goalie John Gibson sustained an upper-body injury Feb. 7 at the Ottawa Senators and was placed on injured reserve Wednesday. Johnson was also placed on injured reserve after being struck in the head by a puck during practice Tuesday.
"It's something you dream of growing up a little kid playing street hockey," said Boyle, who is the first Ducks goalie to get a shutout in his first NHL start since Gibson made 18 saves in a 3-0 win against the Canucks on April 7, 2014. "To be able to come out here and get a win the first game, I can't even describe it."
Jacob Markstrom made 20 saves for Vancouver (25-26-7), which has lost two games in a row. Elias Pettersson's four-game point streak ended.
"We couldn't get a puck in the net," Canucks coach Travis Green said. "If you didn't watch what pucks went in the net tonight, you would've been really happy with our game."