Steve Bruce’s side were made to work hard by their League Two hosts but Aluko and Sagbo struck after the interval to break York's stubborn resistance and settle matters.
The Tigers were matched by their Yorkshire counterparts in what was largely an uneventful first 45 minutes with the only real action of note coming when summer signing Robert Snodgrass saw his goal disallowed after the assistant referee ruled that Shane Long had failed to prevent Ahmed Elmohamady’s cross from going out of play.
Robbie Brady had a opportunity to open the scoring after Long was awarded a free-kick 25-yards from goal following a foul by Marvin McCoy. However, the chance went to waste as the Irishman fired the set-piece over the bar.
Bruce opted to ring the changes at the break, making eight changes, and within five minutes of the restart, the Tigers opened the scoring. Aluko picked the ball up outside the area and let fly with 25-yard effort that crept under the body of Ingham.
The home side responded in positive fashion and came close to levelling the scores when Jake Hyde forced Allan McGregor into making a smart save.
Ince could have made it 2-0 when he was put through one-on-one, only to fire straight at Ingham, before Michael Coulson was denied by the top of the crossbar after latching onto Ryan Jarvis' ball over the top.
The Tigers secured the win with 13 minutes remaining when Sagbo smashed the ball past substitute keeper Jason Mooney following a defensive mistake from Keith Lowe.
Ince almost added a third late on after combining well with Sagbo but the former Blackpool man fired over with a rasping drive from just inside the box.
Hull City: Allan McGregor, Ahmed Elmohamady (Liam Rosenior 46), James Chester (Alex Bruce 46), Paul McShane (Curtis Davies 46), Conor Townsend, Robert Snodgrass (Sone Aluko 46), David Meyler (Tom Huddlestone 46), Stephen Quinn (Jake Livermore 46), George Boyd (Joe Dudgeon 68), Robbie Brady (Tom Ince 46), Shane Long (Yannick Sagbo 46).