After dominating a scoreless first period, the Ducks took the lead 3:19 into the second when Cam Fowler weaved into the offensive zone before dishing off to Silfverberg, who converted a one-timer for his eighth of the season.
Vancouver then had a great opportunity with 58 seconds of a 5-on-3 power play, but Gibson, who was coming of a 39-save performance in Tuesday's 2-1 victory over Montreal, stopped Daniel Sedin on two point-blank chances before Brandon Sutter fanned on a loose puck in the slot.
Anaheim opened a 2-0 lead with 5:25 left in the period when Kase caught Miller out of position before throwing a puck in front that caromed off Vancouver defenseman Nikita Tryamkin, the post and finally Erik Gudbranson before crossing the line for his first goal in his eighth NHL game.
Ryan Kesler, the former Canucks forward who gets booed every time he touches the puck at Rogers Arena, then ripped a shot off the post behind Miller that stayed out in the final seconds of the second.
Vancouver got one back with seven minutes left in regulation when Henrik Sedin finished off a pass from Loui Eriksson at the side of the net after Fowler's clearing attempt took a bad bounce off the glass.
The Canucks continued to press in the final moments, but Cogliano beat Miller for his sixth with 2:35 left as Anaheim closed out a successful opener to its three-game road trip through western Canada.
NOTES: Kase was the 205th pick in the 2014 draft.
Ducks: Visit Edmonton on Saturday night. Canucks: Conclude a three-game homestand Saturday against Toronto.