With recent recruits Tom Ince, Robert Snodgrass and Jake Livermore all featuring at Bootham Crescent, the visitors were made to work hard by their League Two hosts.
However, Aluko and Sagbo struck after the interval to break York's stubborn resistance and settle matters.
Hull were largely matched by their Yorkshire counterparts in the first half, although Robbie Brady went close to opening the scoring when his early effort was disallowed after the ball had curled out of play.
Boss Steve Bruce opted to ring the changes at the break, including introducing Livermore and Ince from the bench.
And within five minutes, the Premier League side were ahead as Aluko picked the ball up outside the area and beat Michael Ingham from 25 yards.
The Northern Irish goalkeeper may feel he could have done better with the shot, but York almost responded immediately when new signing Jake Hyde tested Allan McGregor.
Ince could have made it 2-0 when he was put through one-on-one, only to fire straight at Ingham, but Sagbo made no such mistake as he punished a defensive error with a cool finish 13 minutes from time.