Devin Hester caught one of Cutler's scoring strikes and set an NFL record with his 14th career touchdown return, running back a punt 64 yards for a score as Chicago won in a game played in the snow at the University of Minnesota's TCF Bank Stadium.
Cutler (14-of-24, 194 yards) found Hester on a 15-yard TD toss to put the Bears up 17-7 at the half, and the Chicago speedster made it 27-7 in the third on his record-setting punt return.
Johnny Knox made two grabs for 78 yards, including a 67-yard scoring play, and Matt Forte gained 92 yards on 19 carries for Chicago (10-4).
Brett Favre made a surprise start after originally being ruled out of the game with a shoulder injury.
He went 5-of-7 for 63 yards, a TD and an interception before being taken out of the game with what was called a head injury after being sacked in the second quarter.
Rookie Joe Webb entered and went 15-of-26 passing for 129 yards, two interceptions and a rushing touchdown for the Vikings (5-9).