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.
Justin Bieber crashes Drake Bell's album release party
Members of Congress to keep receiving porn magazine