Kieran McKenna's side made the vital breakthrough at Portman Road when midfielder Azor Matusiwa fired home from the edge of the penalty area in the 71st minute.
Ipswich's third successive victory saw them leapfrog Millwall into third place in the Championship table.
They are three points behind second-placed Middlesbrough, with a game in hand in the race for automatic promotion via a top-two finish.
Hull remain fifth, six points adrift of Middlesbrough, after a first away defeat in nine games stretching back to November.