Fulham trailed at the break at the KC Stadium and had to substitute both goalkeeper Marcus Bettinelli and striker Matt Smith just before half-time.
Ahmed Elmohamady broke the deadlock on 34 minutes when he nodded in from Andy Robertson’s cross to give Hull the lead.
The Egyptian then headed just wide from another Robertson delivery as Hull upped the tempo, and shortly afterwards Bettinelli and Smith collided as they both tried to reach a loose ball.
The two team-mates had to be taken off, replaced by Andy Lonergan and Moussa Dembele.
Smith had had Fulham’s only shot on goal in the first period, a low effort from distance in the 38th minute which was comfortably fielded by City keeper Allan McGregor.
Kit Symons selected an unchanged team from the one which lost 2-1 to Brighton at the weekend, while former Brentford full-back Moses Odubajo was named in the Hull side.
Hull City: McGregor; Odubajo, Dawson, Davies, Robertson; Elmohamady, Meyler, Huddlestone, Aluko; Akpom, Hernandez.
Subs: Jakupovic, Taylor, Clucas, Maguire, Jelavic, Hayden, Luer.
Fulham: Bettinelli; Richards, Hutchinson, Bodurov, Voser; Cairney, Christensen, O’Hara, Pringle; McCormack, Smith.
Subs: Lonergan, Burn, Kavanagh, Tunnicliffe, Kacaniklic, Woodrow, Dembele.