Redman replaced the injured Rashard Mendenhall who hurt his right knee on the final play of the first quarter. He carried 19 times, compiling 92 yards, but also turned the ball over twice late in the game.
Ben Roethlisberger completed 23-of-40 passes for 221 yards while playing the entire game with a sore ankle for the Steelers (12-4), who had to settle for the AFC's No. 5 seed due to Baltimore's win over Cincinnati Sunday.
Pittsburgh will have to go on the road next week to face AFC West champion Denver in the first round.
Cleveland's Seneca Wallace started for the injured Colt McCoy and struggled, completing only 16-of-41 passes for 177 yards and an interception for the Browns (4-12).
2014: The Year in Music [PHOTOS]