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.
Man spent 15 hours in jail for plugging electric car into an outlet at a school
Ron Burgundy interviews Peyton Manning on SportsCenter