Green collected eight boards while Paul George (14 points) and Roy Hibbert (12, nine rebounds, five blocks) also played big roles as the Pacers snapped a two-game skid.
Indiana won despite the injury absence of starting power forward David West.
The Cavaliers got 21 points from reserve C.J. Miles en route to their fifth loss in six games.
Tristan Thompson supplied 20 and 11 boards for Cleveland.