Tomlin became only the third coach Pittsburgh has had in the last 38 years after Bill Cowher stepped down following the 2006 season.
Roethlisberger, who struggled last season after leading the Steelers to the Super Bowl in 2005, completed 12 of 23 passes for 161 yards Sunday. Willie Parker gained 109 yards on 27 carries.
Pittsburgh extended its 17-0 halftime lead when Roethlisberger connected with Matt Spaeth for a five-yard touchdown at the end of a 71-yard drive in the third period, and then threw 22 yards for another score to Heath Miller.
Cleveland's only touchdown came on a one-yard run by Lawrence Vickers that reduced the Browns' deficit to 24-7.