Cleveland kicker Phil Dawson made four field goals and had a pitch shot of 22 yards with just over two minutes to play, but a bad snap caused his kick to knuckle to the left as the Rams held on for a 13-12 win.
Josh Brown kicked field goals of 29 and 34 yards and Sam Bradford hit Brandon Lloyd with a seven yard touchdown pass. Bradford was just 15 of 26 for 155 yards. Steven Jackson rushed for 128 yards on 27 carries.
The Rams improved to 2-7 while the Browns dropped to 3-6.
