The Bears -- who allowed the fewest points in the NFL last year -- handed the Packers their first shutout in 233 consecutive games dating back to Oct. 17, 1991.
Grossman completed 18-of-26 passes and threw one interception. Muhsin Muhammad had six catches for 102 yards, Thomas Jones ran for 63 yards on 21 carries, and Desmond Clark picked up 77 yards on five catches for the Bears (1-0).
Robbie Gould hit on all four of his field goal attempts for Chicago.
Brett Favre completed just 15-of-29 passes for 170 yards with two interceptions. Ahman Green rushed for 110 yards on 20 carries, and Donald Driver caught seven passes for 96 yards for the Packers (0-1), who played their first regular season game under new head coach Mike McCarthy.