David Booth, Aaron Rome, Daniel Sedin and Dan Hamhuis each added power-play goals and Jannik Hansen had Vancouver's only even-strength score as the Canucks (7-7-1) handed the Blackhawks their first regulation home loss.
Vancouver's Roberto Luongo made 38 saves to help the Canucks end a two-game slide.
Chicago's Corey Crawford blocked 32 shots.
Booth's goal was his first this season. He joined the Canucks from Florida in a multi-player trade on Oct. 22.
Rome, who has just three career goals in 132 games, connected in his first game this season after recovering from a broken hand.
The Canucks and Blackhawks met for the first time since Vancouver eliminated Chicago in overtime of Game 7 of an opening round playoff series last April. The teams have faced each other in the postseason for three straight years, with Chicago winning the first two series.
Crawford was sharp and made several quick, point-blank stops in the first period as Vancouver dominated and outshot Chicago 17-9. But Booth, who opened the scoring 6:00 in, was the only Canuck to connect in the frame.
After Crawford make a kick save on Booth's one-time shot from 10 feet out, Booth was left open and popped in the rebound.
Frolik tied it at 1 with 7:03 left on a soft shot from the left wing boards that Luongo misplayed. The 45-foot attempt struck the inside of Luongo's left pad and caromed in between his legs.
The Canucks took charge with four goals in the second.
Rome and Daniel Sedin scored power-play goals 3:24 apart early in the period to make it 3-1.
Rome connected on a screened drive the top of the circle at 1:16. Daniel Sedin fired into an empty net at 4:40 after Crawford had fallen following a collision with Vancouver's Ryan Kesler.
Kruger cut it to 3-2 with 4:53 left in the second by plowing to the net and knocking in a rebound. But Hansen replied from the edge of the crease with Vancouver's only even-strength goal 43 seconds later when Crawford was trapped out of position by teammate Bryan Bickell.
Hamhuis added another power-play goal, shooting in through traffic from the top of the right circle, with 2:10 left in the period to extend the Canucks' lead to 5-2.
Henrik Sedin made it 6-2 midway through the third when he took Alexander Edler's feed and backhanded it in from the edge of the crease.
Notes: The five power-play goals against tied a Blackhawks team record. ... Chicago D Duncan Keith missed his third game with a left hand injury. Keith, who won the Norris Trophy in 2010, is day-to-day. ... Vancouver LW Alexandre Burrows sat out with a back injury suffered Friday in St. Louis. D Sami Salo missed his third game with a groin injury. ... Including regular-season and playoff games, the Canucks and Blackhawks have met 32 times over the past four seasons.