Sunderland's hopes were dealt what proved to be a fatal blow with just four minutes gone when central defender Wes Brown was sent off after felling Long after he had intercepted Phil Bardsley's ill-advised back-pass.
It took Hull until the 16th-minute to make their numerical advantage tell when Long flicked Jake Livermore's scuffed shot into the roof of the net.
The game was over as a contest when Jelavic headed past keeper Vito Mannone after Maynor Figueroa's 62nd-minute shot had looped up invitingly off substitute Santiago Vergini.