After the first two shooters came up empty, Hossa skated in deliberately before firing a heavy slapper from the slot that overpowered Ilya Bryzgalov and slipped across the goal line to put the Blackhawks on top.
Corey Crawford then turned aside the final two shooters with relative ease, as Chicago snapped its three-game slide and moved within one point of Colorado for second place in the Central Division. The Avalanche are currently in action against the New York Rangers.
Charlie Coyle and Erik Haula had a goal apiece for the Wild, who salvaged a point to move five clear of Dallas for the first wild card spot in the Western Conference.
Bryzgalov stopped 24 shots in the setback.