Laurent Blanc's side are unbeaten in the competition this season and look genuine contenders to win the trophy after Michael Ciani nodded home Yoann's Gourcouff's free-kick from close range on the stroke of half time.
Five minutes before half-time Rose made amends, finding space in the box to side-foot home after Carroll had nodded down a deep ball from Michael Mancienne.
It owed much to the hard work of Constable, who beat York keeper Michael Ingham to a long ball over the top, lofting it back into the middle where Jack Midson nodded down to Green who dispatched a sweet left-foot half-volley into the top corner from the edge of the box.