Richardson's score in the third quarter ensured Cleveland only its third win in 25 meetings against the AFC North rival Steelers, who committed eight turnovers in the contest.
Brandon Weeden completed 17-of-26 throws for 158 yards, a TD and an interception for the Browns (3-8), who scored 17 points off the Steelers' errors.
Emergency starter Charlie Batch tossed three interceptions for Pittsburgh (6-5), whose hopes for a division title took a blow heading into a key matchup with the Baltimore Ravens next week.
Starter Ben Roethlisberger missed Sunday's game with injuries to his right shoulder and ribs.
Notable deaths of 2014 [PHOTOS]