Rodgers completed 23-for-36 pass attempts for 291 yards as the Packers (10-4) claimed their second straight division title with their eighth win in nine contests.
Randall Cobb made six grabs for 115 yards in the victory.
The struggling Bears (8-6), meanwhile, saw their playoff hopes put in danger with their third consecutive loss and fifth in six games.
Jay Cutler was limited to 135 passing yards on 12-of-21 efficiency with a touchdown and an interception in the loss.
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