The Devils remained stuck on one victory this season, having suffered four of their nine losses in overtime.
New Jersey grabbed a 2-1 lead through one period on goals by Patrik Ellis and Eric Gelinas, but Vancouver tied it in the second on a slap shot from Daniel Sedin.
That was all the scoring until the shootout started and Santorelli immediately put the Canucks in front by beating Cory Schneider.
Luongo turned aside 28-of-30 shots during regulation and overtime. Schneider, appearing for the fourth time in five games after Martin Brodeur got off to a struggling start this season, made 19 saves.