Chicago, owner of the best regular-season record in the NHL, won the Western Conference quarterfinal series in five games.
The Blackhawks will take on the lowest seed remaining among the teams that reach the conference semifinals and that would be Detroit if the Red Wings can rally from a 3-2 deficit and oust Anaheim.
If that does not happen, Chicago would take on San Jose in the next round.
Hossa scored the only first-period goal and then produced a backhander 6:26 into the second stanza that gave the Blackhawks a 3-0 led.
Corey Crawford had to make just 21 saves to earn the series-clinching victory, a win that evened his career post-season record at 9-9. Crawford led Chicago past the first round of the playoffs for the first time in three tries as the team's front-line goaltender.
Josh Harding started in goal for the Wild after leaving Game 4 with a leg injury. He gave up three goals on 18 shots before being replaced by Darcy Kuemper.