Roethlisberger completed 23-of-35 passes for 417 yards with one interception and his scoring passes led Pittsburgh to a 17-7 halftime advantage.
Jeff Reed kicked two field goals.
Heath Miller caught a touchdown pass, while Rashard Mendenhall added a touchdown on 17 carries for 62 yards for the Steelers (4-2), who have won three in a row.
They held a 543-197 advantage in total offense.
Cleveland's Derek Anderson went just 9-for-24 passing for 122 yards with a touchdown.
Josh Cribbs scored on a 98-yard second-quarter kickoff return and added 45 rushing yards on six carries for the Browns (1-5).
He became the first player since 1950 to return a kickoff for a score and throw an interception in a regular-season contest.