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Nikica Jelavic had the first chance of the match for the home side when a high ball into the box fell for him just a couple of yards out, but his header was too high.
Mutch had another chance to open the scoring when Austin took the ball from Allan McGregor, but the summer signing could not find the target.
Austin was involved again just before the break as he won a corner, but Steven Caulker saw his header cleared off the line.
The stalemate was broken shortly after the restart as Hull won a corner, resulting in Chester losing Rio Ferdinard in the box to head the visitors into the lead.
Rob Green had to make a smart save to stop Hull doubling their lead later in the second half as Tom Ince tried to fire the ball in from a free kick.
The resulting corner presented Jelavic with another chance, but the Croatian's strike was blocked on the line by Richard Dunne.
The hosts were handed a lifeline late on when Austin won a penalty, but the striker's spot kick was saved by McGregor, while a late effort from Bobby Zamora also missed as Harry Redknapp's side suffered defeat on their return to the top flight.