Redman scored on a seven-yard run in the third quarter for the Steelers (12-4), who finished tied with Baltimore for first in the AFC North but lost the tie-breaker because the Ravens beat them twice.
The Steelers had to survive two fumbles by Redman in the second half and a pass into the end zone by the Browns (4-12) on the final play that was batted down.
Mendenhall hurt his right knee in the first quarter on a short run and didn't return. His status for the post-season is unknown.
Pittsburgh quarterback Ben Roethlisberger passed for 221 yards on a severely sprained ankle.