Campbell amassed 262 aerial yards on 23-for-35 efficiency for the Browns (4-5), who last beat the Ravens on Nov. 18, 2007.
Davone Bess hauled in two of Campbell's scoring strikes and Gary Barnidge snagged another as Cleveland broke an overall three-game skid.
Greg Little led the Browns' receiving corps with seven grabs for 122 yards.
The defending Super Bowl champion Ravens (3-5) dropped a third straight despite a good game from quarterback Joe Flacco. He went 24-of-41 for 250 passing yards with two touchdowns and an interception, and also gained 25 rushing yards on three tries.