Green's 48-yard touchdown catch on the final play of the first half helped the Bengals (3-4) regain their footing in the injury-depleted AFC North.
The defending division champions piled up their most points since they beat the Browns 37-3 last December. Jeremy Hill had a 74-yard touchdown run as part of his 168-yard effort, the best by a Bengals running back in seven years.
The Browns (0-7) extended their worst start since 1999, when they were a first-year expansion team. The NFL's only winless team also lost yet another quarterback — the theme of their season.
Cody Kessler got hit hard while throwing a shovel pass in the second quarter, then went to the locker for a concussion evaluation and was ruled out.
That left the offense in the hands of undrafted rookie Kevin Hogan, the Browns' sixth quarterback of the season.
Hogan — Cleveland's last quarterback standing — kept it close for a while by scrambling 28 yards for his first NFL touchdown. He finished as the Browns' top rusher with 104 yards.
With cornerback Joe Haden sidelined, the Browns had nobody who could cover Green, who had eight catches for 169 yards. The entire Browns defense couldn't stop him on the final play of the first half.
Green showed his dexterity by juggling three oranges on the postgame show after a Thursday night win over the Dolphins earlier this season. His latest juggling act counted. Green reached with his right hand and pulled in the tipped ball for a 21-10 halftime lead.
He also had a 48-yard catch down the sideline that set up a field goal as the Bengals pulled away in the third quarter.
