Luongo has 57 shutouts over 12 seasons, including a career-best nine during the 2008-09 campaign. He has started 15 of Vancouver's last 17 games.
Daniel Sedin opened the scoring with his 18th goal of the season 6:42 into the first and Alex Burrows increased the lead midway through the opening period.
It remained a 2-0 contest until Manny Malhotra scored into an empty net with 29 seconds to play. Vancouver snapped a two-game skid.
Minnesota continued to let an excellent start to the season slip away. The Wild lost for the 10th time in 11 games after winning 20 of their first 30 contests.