Terry (1-1=2) extended his streak with an assist on the game's opening goal. The 24-year-old became the fifth Duck with points in 12 straight, joining Paul Kariya, Teemu Selanne, Ryan Getzlaf and Corey Perry. Terry's scoring run is the longest by a Duck since 2013.
Gibson stopped 41-of-43 shots to post his fourth straight win.
"John came into camp with a great attitude," Getzlaf said. "If you saw him work in practice, it really sheds light for me. Those are the areas where Gibby drives our team and drives us to be better, and it shows. The result is out there. The guys rally around him. We have all the faith in the world in him."
Cam Fowler and Isac Lundestrom also scored for Anaheim.
The Canucks controlled the better of play in the first period, but Gibson stood tall with 13 saves to keep the home team off the board.
The Ducks took advantage of their netminder's stellar start to the evening, capitalizing on the power-play to to take the lead. Terry poked a loose puck along the wall to Fowler at the right point, where the Anaheim blueliner played catch with Sonny Milano along the edge of the zone. Fowler eventually found some open space between the circles, drifting into the slot and firing a wrist shot by Vancouver netminder Jaroslav Halak to put the Ducks ahead.