Manager Steve Bruce was at North Ferriby and Hull took the lead against the Conference North club on 14 minutes when Stephen Quinn and Robbie Brady combined for Leroy Rosenior to convert a low cross.
The Premier League side increased their lead three minutes before half-time when striker Nick Proschwitz finished at the second attempt after his initial header had been saved.
North Ferriby pulled a goal back through Nathan Jarman, but Quinn wrapped up the win for the Tigers by scoring the third goal a minute from time.
At Winterton, a hat-trick from Matty Fryatt was the highlight as the Tigers started with a 3-5-2 formation in both matches.
David Meyler opened the scoring after just five minutes and, two minutes later, Fryatt was on target for the first time.
Fryatt then saw a penalty saved before he made it 3-0 four minutes before half-time after Winterton had failed to deal with Sone Aluko's corner.
The Tigers scored again before the interval through Corry Evans, and early second-half goals from James Armstrong and Fryatt rounded off the scoring.