Korpikoski scored the only goal in the shootout in the third round to lift Phoenix to its 10th consecutive home win.
Ed Jovanovski and Petr Prucha scored in regulation for the Coyotes, who remain hot on the heels of Pacific Division-leading San Jose. Jason LaBarbera made 28 saves and halted Mikael Samuelsson's third-round try in the shootout to end the Canucks' three-game winning streak.
Samuelsson and Kyle Wellwood tallied Vancouver's goals. Roberto Luongo made 23 saves.
Phoenix took a 1-0 lead on Jovanovski's power-play goal at 10:00 of the second period but Samuelsson tied it 49 seconds later. Phoenix then regained the lead on Prucha's goal at 17:02.
Wellwood tied the game 2-2 with 6:31 remaining in the third period. The Coyotes kept the Canucks at bay despite being shorthanded for the final 51 seconds of regulation and the first 1:09 of overtime.