Art Modell, who moved the Browns' storied franchise to Baltimore five years ago, was not in attendance to witness the latest defeat for his suddenly struggling Super Bowl champions.
The Ravens had won the four previous meetings from Cleveland, the last three by a combined score of 97-16. But Baltimore fell to 3-3 while the surprising Browns (4-2) moved into sole possession of second place in the AFC Central under rookie coach Butch Davis.
Couch hit wide receiver Kevin Johnson with a 28-yard touchdown to cap a nine-play, 80-yard drive and give the Browns a 17-6 advantage midway through the third quarter.
Defensive end Greg Spires highlighted his active day by recovering a fumble by Ravens quarterback Elvis Grbac at the Baltimore 36. On the next play, Couch found rookie receiver Quincy Morgan in the end zone to open an 18-point cushion.
Enjoying solid protection from his offensive line, Couch had time to complete 11 of 18 passes for 149 yards with no interceptions. The third-year quarterback's performance came a week after the Ravens' daunting defense was humbled by three-time Most Valuable Player Brett Favre in a road loss to the Green Bay Packers.
Cleveland rookie James Jackson gained 77 yards on 24 carries, including the opening touchdown, against Baltimore's top-ranked run defense.
Veteran quarterback Randall Cunningham entered the game in relief of a roughed-up Grbac, who had x-rays taken following a blow to the chest. Those x-rays were negative. Grbac sustained a mild concussion last week at Green Bay.