كتب : Sherif Tarek
The 26-year-old was included in the visitors' starting eleven and was taken off in the 70th minute.
Zaki's presence wasn't felt at all till he made way for Jan Vennegoor of Hesselink.
Mikel Arteta put Everton ahead on 17 minutes, before the home side's slender lead was canceled out by a Tom Cairney strike two minutes past the hour mark.
But Arteta regained Everton's one-goal advantage six minutes from halftime.
Hull's Richard Garcia headed into his own net on 51 minutes, before Landon Donovan and Jack Rodwell completed the hosts' rout in the last ten minutes.
Relegation-threatened Hull are in 18th place with 24 points, while Everton lie eighth on 41.