Rodgers logged a 28-of-38 passing efficiency, rolling up 297 yards in a rematch of last year's NFC title game.
Rodgers hooked up with Finley for two touchdowns in the game's first 18 minutes and Ryan Grant rushed for 92 yards on 17 carries for the Packers (3-0), who notched their ninth straight win dating back to last season.
Greg Jennings hauled down nine passes for 119 yards for Green Bay.
The Bears (1-2), meanwhile, lost their second straight game despite Jay Cutler's 302 passing yards and two touchdowns.
The Chicago signal-caller was picked off twice, however.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut