With the Browns trailing 9-7 late in the second quarter, Holcomb threw a pass that was intercepted by free safety Aenas Williams, who returned it 46 yards for a touchdown. Two plays later, Williams intercepted another Holcomb pass and returned it 27 yards to the Browns' 20 to set up a 16-yard touchdown pass from Marc Bulger to Isaac Bruce two plays later to extend the Rams' lead to 23-7.
Couch replaced Holcomb for the rest of the game and completed six of nine passes for 98 yards and one touchdown.
The Browns have lost three straight games to slip to 4-9. The Rams have won nine of their last 10 games to remain in first place in the NFC West Division with a 10-3 record.
"That's what cost us the game," Holcomb said. "It doesn't feel very good to me right now. That's unacceptable and it ended up costing us the game. He (Williams) made two pretty good plays. You can't do that."
Holcomb, who was benched the previous week against Seattle, completed 10 of 17 passes for 80 yards. Couch added some life to the offense when he threw a 28-yard touchdown pass to Morgan at the 10:31 mark of the third quarter. Couch tried to connect with Morgan for the extra two points, but the pass was broken up.
The Rams countered with a 12-play, 44-yard scoring march. Jeff Wilkins kicked a 37-yard field goal with 3:53 remaining in the third period to extend the St. Louis lead to 26-13.
Cleveland marched 83 yards on 11 carries on their next series. White ran 2 yards for the touchdown, cutting the Rams' lead to 26-20.
The Rams moved into scoring territory on their next possession, but a 39-yard attempt of a field goal by Wilkins was wide left. The Browns weren't able to sustain their next drive, forcing a punt that gave the Rams the ball at their 20.
Cleveland's defense stiffened, forcing a punt that Northcutt returned to the Rams' 48. On fourth down, Couch was sacked by Brian Young on fourth down to seal the win for St. Louis.
The Rams opened the scoring with a 28-yard field goal by Wilkins on their first possession. The Browns moved 72 yards on their next series to score on a 2-yard pass from Holcomb to tight end Keith Heinrich.
Cleveland's defense kept the score close by stopping two St. Louis drives that resulted in field goals of 26 and 29 yards by Wilkins.