Before Longwell's game-ending heroics, Minnesota (2-3) was sparked by rookie running back Adrian Peterson, who scored on three long runs, gained a franchise-record 224 yards on 30 attempts and set up the winning field goal with a 53-yard kickoff return.
Longwell also booted a 48-yarder earlier in the fourth.
Chester Taylor added 83 yards rushing on 22 carries as the Vikings snapped a six-game skid against the Bears in Chicago.
Cedric Benson gained 67 yards on 18 attempts, but Chicago (2-4) sank to last place in the NFC Central after the third loss in its last four games.
Swim Week Miami Beach 2014 [PHOTOS]