Cutler also connected with Hester on a go-ahead, 19-yard TD pass with 44 seconds left in the first half, giving Chicago (6-3) the momentum it needed to post the win and tie Green Bay atop the NFC North Division.
Cutler finished the game 22-of-35 in passing attempts for 237 yards, surviving a pair of interceptions.
Brett Favre completed 18-of-31 passes and was limited to just 170 yards with three interceptions and a lost fumble for Minnesota (3-6), which dropped its eighth straight regular-season road game.
Percy Harvin hauled in a 53-yard scoring pass for the Vikings but appeared to suffer a knee injury late in the game.
Notable deaths of 2014 [PHOTOS]