Luongo kept the Wild off the scoreboard until 13:03 of the second period when Devin Setoguchi scored Minnesota's only goal on a power play.
The loss snapped Minnesota's two-game winning streak and extended their record of futility at Rogers Arena to 0-9-2.
Kevin Bieskal and Jannik Hansen scored for the Canucks, who have won six consecutive games.
Darcy Kuemper stopped 28-of 30 shots in the nets for the Wild. Kuemper was called up from the American Hockey League to fill in for Josh Harding, who missed the start due to illness.