The home side were the better side in the first half, but it was still the visitors who had the better of the chances.
Steve Howard had an early goal disallowed for a foul by a team-mate, while on the half-hour Andy King's shot from a packed penalty area came back off the home post before Paul Dickov's low shot brought a good one-handed save from home keeper Arran Lee-Barrett.
James Brown got through for three shots on the City goal, none of them giving keeper Paul Henderson too much trouble, while Richard Barker and Sam Collins both headed off target.
City took the lead six minutes into the second half, Howard cutting in from the left before his mis-hit low shot trickled inside the near post and Nicky Adams finished well from 15 yards after a pass from sub DJ Campbell to make it 2-0 to City after 66 minutes.
And the Foxes broke out for a third three minutes from time when Campbell fed fellow sub Matty Fryatt for a simple tap-in.