It was the 65th shutout of Luongo's 14-year career, the last eight of which have been spent with the Canucks.
The game was almost half over before Daniel Sedin produced the first goal, one that came on the power play.
Vancouver broke things open with third-period goals from Zack Kassian, Chris Higgins and Dale Weise.
All four goals were charged to Devan Dubnyk, who faced 40 shots. Dubnyk came into the game with a 3.36 goals-against average.