The result ensured the home side snapped a four-game losing streak, and allowed them their fifth consecutive win over their AFC North rival, as they moved to 3-5 ahead of their bye week.
Chubb finished with 101 yards on 23 carries and now leads the league with 841 yards through the season's first eight weeks.
Cleveland's secondary, led by defensive end Myles Garrett, sacked Cincinnati quarterback Joe Burrow five times to keep him winless against the Browns.
The Bengals had scored in 41 consecutive halves until the Browns kept them to zero through the first half.
The visitors had also not allowed a touchdown in the second half all season until Cleveland piled on a pair of scores after the big break to put the game to bed.