Seth Jones and Matt Calvert scored, Nick Foligno had two assists, and Sergei Bobrovsky made 24 saves for Columbus.
Jones put the Blue Jackets ahead 1-0 on the power play at 4:33 of the first period with his eighth goal.
"I like how we stuck with it," Green said. "There wasn't a sense of panic on the bench even though the shots were 8-1, or 8-2 (for Columbus)."
Baertschi tied it 1-1 at 1:19 of the second with a power-play goal. Vanek, at the right post, sent a behind-the-back pass across the front of the goal to Baertschi for his ninth goal.
"You score one on the power play, you need your penalty kill to step up," Foligno said. "Tonight we didn't do that. It cost us."
After a Blue Jackets turnover, the Canucks kept the puck in the zone, and Gudbranson scored from the right point with Sedin setting a screen in front to make it 2-1 at 5:38.
It was Gudbranson's first goal of the season in his 31st game.
"We got some bad bounces." Jones said. "We gave them some opportunities and they capitalized on them."
Gaunce broke his stick scoring on the power play to make it 3-1 at 14:31. Edler scored at 17:15 for a 4-1 lead.
Calvert tipped Scott Harrington's shot to make it 4-2 at 12:35 of the third period.