Green made an acrobatic catch of a high pass from Andy Dalton, then sprinted to the left sideline before being pushed out of bounds at the 2-yard line as time was running out.
Mike Nugent followed by connecting on a 26-yard field-goal attempt, giving Cincinnati (7-4) its first lead of the game in the final minute.
Nugent's kick came after Cleveland's Phil Dawson had missed a 55-yarder on the previous possession.
Dalton racked up 270 passing yards and a touchdown and Green finished with three catches for 110 yards as the Bengals snapped a two-game losing streak.
Peyton Hillis returned to the lineup for the first time in six games, rushing for 65 yards on 19 carries, but it wasn't enough for the Browns (4-7).
Colt McCoy passed for 151 yards, two touchdowns and an interception in the loss.
Notable deaths of 2014 [PHOTOS]