Howard opened the scoring after just seven minutes when he got on the end of Matt Fryatt’s chipped cross.
And Andy King doubled the Foxes’ advantage midway through the first half as he slotted home from close range.
Brian Laws made changes at the break and they seemed to be working as Sean McAllister came close to pulling one back for Wednesday, but his goalbound shot was well blocked by Michael Morrison.
Yet Leicester were still being allowed to press forward and almost got their third through shots from Oakley and Fryatt.
And City’s marked improvement on recent performances was complete when the Wales international King grabbed his second of the match to secure the three points.