Alexander Edler opened the scoring with 1:05 left in the second period and Jason Jaffray made it 2-0 1:36 into the third. Michael Grabner added a power-play goal 6 minutes later, and Ryan Shannon scored with 21 seconds left for the Canucks (1-0-1).
Luongo and fellow star goalie Miikka Kiprusoff made their first appearances of the preseason, but neither finished the game.
Luongo made 14 saves in 1 1/2 periods before giving way to Schneider, who stopped seven shots in his professional debut after three standout seasons at Boston College.
Kiprusoff stopped 14 of 15 shots before Curtis McElhinney took over for the Flames (0-2-1) to start the third period.
McElhinney, who played all of a 3-2 shootout loss to Florida on Tuesday in Saskatoon, stopped the first shot he saw. But Jaffray corralled the rebound out of the air and knocked it in. McElhinney finished with two saves.
Copyright by STATS LLC and The Associated Press
Arena: Rogers Arena Location: Vancouver, British Columbia
No scoring this period
Alexander Edler Assist: Markus Naslund, Patrick Coulombe
Jason Jaffray Assist: Michael Grabner
Michael Grabner (power play) Assist: Lukas Krajicek, Mattias Ohlund
Ryan Shannon (power play) Assist: Alexander Edler, Cory Schneider