Grossman completed just 7 of 14 passes for 142 yards for the Bears (4-5) after Brian Griese left the game in the first half with a shoulder injury. Griese ended 10-of-14 for 97 yards.
Berrian caught four times for 89 yards, while Cedric Benson ran for 76 yards and one touchdown.
Robbie Gould also kicked a 32-yard field goal for Chicago.
Josh McCown completed 14 of 27 passes for 108 yards with an interception for Oakland (2-7), which has now lost its last five games.
Sebastian Janikowski booted field goals of 52 and 37 yards to account for the Raiders' only points.