Romo connected on 17-of-34 throws and Barber carried 28 times in the Cowboys' first win at Lambeau Field.
Felix Jones scored on a 60-yard run and Miles Austin caught two passes for 115 yards and a touchdown for Dallas (3-0).
Aaron Rodgers completed 22 passes for 290 yards and ran for a touchdown for the Packers (2-1).
Green Bay's Greg Jennings hauled in eight passes for 115 yards.
Notable deaths of 2014 [PHOTOS]