John Gibson made 28 saves for the Ducks (24-30-7), who are 2-4-2 in their past eight and have been outscored 11-1 in their past three home games.
"He was real solid, especially when we had a couple times there where we iced the puck," Ducks coach Dallas Eakins said. "We had guys tired on the ice and they had fresh ones. He was able to hold us in there when needed, and that's what we need from Gibby every night."
Compher scored at 16:38 of the second period. Colorado forward Martin Kaut stole a clearing pass by Ducks defenseman Hampus Lindholm at the Anaheim blue line and fed Compher for the one-timer.
It was the first NHL point for Kaut, who made his NHL debut on Wednesday.
"I thought we were way better tonight with our compete level," Eakins said. "I thought we were much more physical, which was good. We were structurally good, but we couldn't get one past that goalie."