Despite the possession being evenly shared during the first half at the KC Stadium, the home side enjoyed the better of the chances.
Nick Barmby's side took the lead through an Aaron McClean strike after 27 minutes as Ipswich struggled to contain the powerful forward.
Midfielder Tom Cairney doubled Hull's advantage five minutes later with a 30-yard strike to give his side a 2-0 lead at the halfway stage.
Substitute Jason Scotland managed to pull a goal back for Ipswich in the second half after good work from Jay Emmanuel-Thomas.
Hull replied to the setback with a chance of their own but McClean failed to find the target from inside the box.
Cameron Stewart put the tie beyond doubt in the final minute of stoppage time as his strike from inside the penalty area found the net.