Barber, who started 10 of the Cowboys' first 11 games before he was sidelined with a calf injury, saw action in Saturday's game.
Jones started the Cowboys' previous last three games, totaling 194 rushing yards and 97 receiving yards with one rushing touchdowns.
Cowboys wide receiver Roy Williams is active; he had been listed as questionable with a groin injury.
For the Cardinals, linebacker Joey Porter and kick returner LaRod Stephens-Howling are inactive. Porter, sidelined by a triceps injury, was replaced by rookie O'Brien Schofield because of a triceps injury. Andre Robert handled kick return duties.