The veteran striker donned the keeper's jersey after 50 minutes when Greg Fleming was shown a straight red card for hauling down Matty Fryatt inside the 18-yard area.
But Fryatt failed to capitalise when he drove the penalty wide and 39-year-old Windass went on to defy Leicester with a string of fine saves.
In the first half City had gone close when a Steve Howard shot hit the inside of a post.
Windass then came to Oldham's rescue when he palmed an Andy King shot against a post and then blocked Fryatt's follow up shot.
The Latics might have been awarded a penalty themselves after 58 minutes when Michael Morrison appeared to trip Chris Taylor inside the box.
And right at the death Oldham almost pulled off a stunning win but were denied when David Martin made an instinctive block to keep out Reuben Hazell's close-range header.