Tranmere had the boost of an early goal, but the visitors levelled just before half time before two goals in seven minutes put them in the clear.
It was a bitter disappointment for Tranmere who failed to deliver at a vital stage.
They were given the boost of an eighth-minute lead when Ryan Taylor fired home a 30-yard free-kick.
City almost levelled in the 52nd minute but home keeper John Achterberg produced a tremendous stop from a powerful close-range header by Leon Cort.
It did become 1-1 in the 43rd minute. Kevin Ellison got the better of Ian Sharps and Ian Goodison after a long clearance and rounded Achterberg to net easily.
Tranmere had a penalty appeal turned down right on half time when Eugene Dadi appeared to be tripped, but in fact he was booked for diving.
Hull went ahead on 63 minutes with a well placed left-foot shot by ex-Rover Jason Price after he was put clear by Allison.
New signing Craig Fagan was introduced on the hour and cut inside from a Price pass to open his account with a left-foot effort.
The crossbar denied Allison on 72 minutes with Price heading over from the rebound.
Tranmere finished strongly but could find no way through with City keeper Boaz Myhill making an important late save from Iain Hume.