Ed Reed scored on a 32-yard runback after making one of the interceptions.
Baltimore limited the Browns to 169 yards total offense.
Le'Ron McClain ran for 66 yards and two touchdowns and Willis McGahee added 64 yards and a touchdown for the Ravens (2-0).
Baltimore rookie quarterback Joe Flacco passed for 129 yards and was intercepted twice.
Cleveland quarterback Derek Anderson, under constant pressure by Baltimore defenders, passed for 125 yards and a touchdown.
Jerome Harrison caught a 19-yard touchdown pass for the Browns (0-3).
Notable deaths of 2014 [PHOTOS]