It was the Browns' third win in four but they still need help to reach the post-season and can be eliminated on Sunday if Pittsburgh, Indianapolis and Tennessee all win.
Browns quarterback Baker Mayfield threw two touchdowns, finding Breshad Perriman with a 31-yard touchdown pass and then Antonio Callaway for a two-yard touchdown in the fourth quarter.
AFC South leaders the Houston Texans made it 10 wins in 11 games with a 29-22 triumph at the New York Jets.
Deshaun Watson found DeAndre Hopkins with a 14-yard touchdown pass with 2:15 remaining on the clock to prevent the Texans slipping to a second successive defeat following a nine-game winning streak.
Watson finished with 294 yards and two touchdown passes to Hopkins.