Green-Ellis, who played for the Pats from 2008-11, bulled into the end zone from one yard out on fourth down with 9:21 left in the game, putting the Bengals up 13-3. The lone scoring play came at the end of a 14-play, 93-yard drive.
He finished with 67 rushing yards on 19 carries while Andy Dalton went 20-of-27 through the air for 212 yards and an interception for the Bengals (3-2), who stayed unbeaten at home.
Tom Brady marched the Patriots (4-1) to a 19-yard field goal with 6:28 to play, but could get them no closer, even after rookie running back Giovani Bernard coughed up the ball at the Cincinnati 46 in a driving rain storm with 1:48 remaining.
Brady failed to throw a touchdown pass for the first time 52 games, snapping the second-longest such streak in NFL history.
Notable deaths of 2014 [PHOTOS]