The previous record was 261 yards on 10 catches by Josh Gordon in a 2013 defeat to the Jaguars
Cooper became the second NFL player after Terrell Owens to have 200 receiving yards with three clubs.
Cooper became the first Browns wide receiver to record successive 1,000-yard seasons with 1,265 yards. Only Hall of Fame tight end Ozzie Newsome had multiple 1,000-yard seasons with the Browns.
The Browns played much of the game without kicker Dustin Hopkins, who injured his left hamstring chasing down Dameon Pierce on a 98-yard kick return for a touchdown
Flacco completed 27-of-42 for 368 yards with three touchdowns and two interceptions. In his fourth game with Cleveland, Flacco joined Josh McCown as the only Browns players to pass for 300 yards in three straight games.
Houston's offense remained mired until Davis Mills entered late. Mills went 15-of-32 for 149 yards and two touchdowns, while Keenum was 11-of-17 for 62 yards with two interceptions. Mills had played occasionally in the first half, but Keenum was the apparent starter, largely to Houston's detriment.
The Browns improved to 10-5 with the win. Since returning to the league in 1999 as an expansion club, this is the team's third 10-win season and second under Stefanski. As the AFC's No. 5 seed, Cleveland can secure a postseason position by beating the Jets on Thursday. The season ends in Week 18 against Cincinnati.
At 8-7, Houston is still in the postseason hunt, but it's harder. At No. 8 in the AFC, the Texans will play the Titans at home next week before completing the season at Indianapolis in Week 18. Positively, Houston quarterback C.J. Stroud may return next Sunday.