After picking up 193 yards through the air and crossing for a rushing touchdown against the Los Angeles Chargers last week, Burrow looked even more comfortable in his second game.
The number one overall pick threw for 316 yards and three touchdowns against Cleveland, however Cincinnati's defence struggled against Cleveland's diverse offence and a much-improved Baker Mayfield.
The Browns quarterback bounced back from a lacklustre effort against the Baltimore Ravens in week one to throw for two touchdowns.
Meanwhile the Bengals were unable to contend with Cleveland's ground game, as Nick Chubb crossed for two touchdowns and Kareem Hunt finished with one.
Hunt also picked up a receiving touchdown along with Odell Beckham Jr.