Henrik Sedin scored a goal and added two assists to extend his points streak to three games and twin brother Daniel added three assists to help the Canucks win for the 11th time in 14 games.
At 20-9-5, the Wild are off to their best start in franchise history, even after their fourth straight loss.
Despite missing five key forwards to injury, the Wild controlled most of the play in the first period while outshooting the Canucks 13-9. But Vancouver held a 1-0 lead after 20 minutes and then built its lead to 3-0 after the second.
Luongo was tested early as a Dany Heatley's slid just wide of the post 10:30 into the game and Pierre-Marc Bouchard's slap shot required a difficult save.
Henrik Sedin opened the scoring on a power play at 18:52 of the first as he fired off a cross-ice pass from Daniel.
The goal came after Vancouver defenseman Alex Edler made a great play at the other end of the ice, racing back to check Matt Cullen as he rushed alone toward the Vancouver net with the puck.
Kesler put the Canucks ahead 2-0 on another power play midway through the second period. He fired in Daniel Sedin's pass from behind the net as the Swede waited patiently before sneaking a puck through a defender to Kesler on the edge of the crease.
Minnesota's Heatley was off for high-sticking after he swatted at a Bouchard point shot that Luongo had caught during a Wild power play and then clipped Burrows in the face.
Burrows gave the Canucks a 3-0 advantage with just over two minutes left in the second. He put in Daniel Sedin's pass from the side of the net, culminating a three-way passing play with the twins.
Luongo preserved his shutout with just under four minutes left in the game as he stopped a Colton Gillies backhand following a giveaway deep in the Vancouver end. Moments later, Hansen closed out the scoring.
The Wild suffered its ninth straight loss in Vancouver since last winning Jan. 31, 2009. Minnesota has gone 0-7-2 at Rogers Arena since then.
NOTES: Canucks winger Mason Raymond left the game midway through the third period after he took teammate Kevin Bieksa's clearing attempt in the face ... Bouchard returned to the Minnesota lineup after missing two games with a broken nose. ... Canucks D Aaron Rome is out three-to-four weeks with a broken thumb suffered Saturday while blocking a shot in Toronto. D Keith Ballard sat out with back spasms stemming from a flare-up of an injury that forced him to miss the last five minutes of Saturday's game. He took part in the morning skate but the back did not loosen up sufficiently, associate coach Rick Bowness said. ... RW Jed Ortmeyer played for Minnesota a day after being called up from Houston of the AHL.