Nikolaj Ehlers, Josh Morrissey and Blake Wheeler also scored, and Connor added two assists for the Jets. Andrew Copp added three assists, and Winnipeg won for the third time in four games to get within five points of the Western Conference's final wild-card spot.
Jonathan Toews, Dylan Strome, Taylor Raddysh and Philipp Kurashev each scored for Chicago. Patrick Kane set up the goals for Strome and Raddysh.
Chicago goalie Marc-Andre Fleury made 26 saves while the subject of trade rumors less than 24 hours before the deadline.