Winnipeg has dropped its first two games since moving from Atlanta following the 2010-11 campaign. The Jets let a two-goal lead slip away in its bid for an initial victory.
After Hossa then scored the go-ahead tally, Dave Bolland produced his third goal of the young season for a 4-2 lead.
Ondrej Pavelec, who allowed five goals in his first start of the season, stopped 28 shots.
The Blackhawks won their second straight at home after losing on the road to open the season.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Exploding whale video goes viral on Internet