Johnson made it 2-1 at 13:17 with a one-timer after a stop-and-spin drop pass off the rush by Nathan MacKinnon, who had two assists.
"Even when they scored goals, I thought our response was really good," Demko said. "That's something we can build on. Closing games out is really important."
MacEwen put Vancouver ahead 3-1 with a wrist shot on a partial breakaway 2:12 into the second period, but Landeskog made it 3-2 at 3:23, and Valeri Nichushkin tied it 3-3 at 8:04 when he scored on a 2-on-1.
"It was back and forth, really good pace, it was competitive and physical, which I like to see from our group," Bednar said. "But it's a game of mistakes, and the ones we made today were pretty big ones."
Antoine Roussel redirected a centering pass from Adam Gaudette through Francouz's legs from in tight at 12:17 to give the Canucks a 4-3 lead.