Cincinnati nearly opened the scores in spectacular fashion after Andy Dalton made a big 57-yard pass play to Green, who looked like he was free to run it home but he was brought down by Tramon Williams.
However, it did not stall the drive and after they completed a fourth-down play in the redzone, Dalton kept the ball to run the ball into the endzone for a touchdown.
The Bengals went further in front as Dalton connected with Green twice for two 20-plus yard pass plays and the second saw the wide receiver add another six points to the score.
The visiting team extended their lead in the second quarter as Mike Nugent split the uprights twice, from 44 yards and 40 yards out respectively, to make it 20-0.
Travis Coons made sure the home side did not go in scoreless as the Browns kicker nailed a 47-yard field goal to reduce the deficit to 17 points at the break.