Dalton racked up 318 yards while A.J. Green hauled down seven passes for 58 yards and a score for the Bengals (1-1).
Andrew Hawkins and Brandon Tate each reeled in a scoring pass from Dalton as Cincinnati doused its intrastate rival for the seventh time in eight meetings.
Rookie Brandon Weeden completed 26-of-37 pass attempts for 322 yards and two scores with no interceptions in his second career game for the Browns (0-2).
Fellow 2012 first-round draft choice Trent Richardson ran 19 times for 109 yards, notching both rushing and receiving touchdowns in the loss.