Fellow summer arrival Martyn Waghorn also broke his duck for the Rams as Frank Lampard’s outfit won the battle of the second strings in front of a sparse crowd. Mason Mount added a late fourth to complete the rout.
Hull will hope more fans turn up on Saturday when the clubs do it all over again with Championship points up for grabs.
Four academy graduates started for Hull while Derby had the likes of former Tigers midfielder Tom Huddlestone and experienced defender and captain Richard Keogh in their starting side.
Both teams showed numerous changes with the home side numbering nine and the visitors eight.
The visitors took the lead their dominance deserved after 24 minutes when a ball over the top from Bradley Johnson played Waghorn through and he took it on his chest before lobbing George Long.
The visitors were two goals to the good seven minutes before the break as Jozefzoon was given too much space on the edge of the Hull area and shot home.
Substitute Duane Holmes crossed low for Jozefzoon to net his second after 73 minutes and Mount added a fourth.
Hull City: Long, McKenzie, MacDonald, Curry, Kane (Milinkovic 59), Batty (Sheaf 69), Stewart, Toral, Fleming, Keane, Dicko. Unused substitutes: Marshall, De Wijs, Burke, Bowen, Kingsley.
Derby County: Roos, Wisdom, Keogh, Tomori, Malone (Lowe 71), Mount, Huddlestone, Johnson (Bird 80), Marriott (Holmes 71), Waghorn, Jozefzoon. Unused substitutes: Carson, Forsyth, Bennett, Nugent.
Referee: Oliver Langford (W Midlands).