Jake Virtanen scored twice for his first NHL multigoal game, and Jacob Markstrom made 24 saves for the Canucks (8-6-0).
"I felt like I was pretty confident tonight," said Virtanen, who scored against the Wild.
Brandon Saad and Jonathan Toews scored, and Crawford made 24 saves for the Blackhawks (6-4-3), who were without leading scorer Patrick Kane because of illness. Kane's 11 goals are tied with David Pastrnak of the Boston Bruins for the NHL lead, and his 18 points are the most on Chicago.
"You can't replace him, but at the same time, you have to be sharper with [your] details because you are missing one of the best players in the world," Saad said of Kane, who had not missed a game since returning for the Stanley Cup Playoffs after breaking his left clavicle Feb. 24, 2015. "Definitely it hurts, but that's still no excuse to play that poorly with the puck."
Turnovers were a problem for the Blackhawks, who are 0-2-1 their past three games.
"It was self-inflicted on the goals-against," coach Joel Quenneville said. "Preventable, all of them, and they turned turnovers into the back of the net."
Saad gave Chicago a 1-0 lead at 6:56 of the first period, but Virtanen tied it 1-1 at 15:33 when he scored on a breakaway with a wrist shot over Crawford's glove.
Toews scored with a wrist shot through a screen on the power play 1:05 into the second period to make it 2-1. It was his seventh goal, second in the past 10 games, and the sixth of the season for Chicago's 26th-ranked power play.
Saad almost scored on a shorthanded breakaway at 9:30 of the second, but he hit the crossbar before kicking the rebound into the net.
"I could have had a couple more," Saad said. "A couple posts and unlucky bounces, but regardless we have to tighten up defensively. We give that team that much rush chances and time and space, and they are going to capitalize."
Virtanen tied it 2-2 at 12:24 with a quick wrist shot off the rush from the left face-off dot that went over Crawford's blocker. Markus Granlund made a backhand pass to Virtanen while falling to the ice after being hooked by Manning.
Virtanen said he's been inspired by Elias Pettersson, Vancouver's 19-year-old rookie forward who has seven goals in his first eight NHL games.
"I watch Petey pretty closely," the 22-year-old said. "You see a young guy come in and score goals, and it boosts you a bit. You want to keep up with a so-called young guy."