Athletic were reduced to ten men after 50 minutes when Greg Fleming was shown a straight red card for hauling down Matt Fryatt inside the 18-yard area.
But the usually lethal Fryatt lost his duel with Windass when he failed to captialise with the spot-kick which he drove wide of the stand-in keeper's right-hand post.
Windass then came to Oldham's rescue just a moment later when he palmed an Andy King shot against a post then bravely dived to block Fryatt's follow-up effort.
It was the first of a string of fine saves by 39-year-old Windass, who performed heroics again close to the end when he beat away yet another Fryatt shot.
Leicester carved out a great chance 20 minutes when Sean Gregan was robbed by Steven Howard whose drive hit the inside of a post.
The ball then rolled across the face of the goal but no City player was near enough to apply the finishing touch.
Fryatt had two chances in as many minutes before the break when he curled a shot narrowly wide before he fired over from a tight angle.
On the stroke of half-time, Manchester United trainee Tom Cleverley seized on a defensive error and rounded the keeper but was thwarted by Scott Golbourne's brave goalline clearance.
Athletic had to be applauded for taking the game to City despite being reduced to ten men.
They were left fuming on 58 minutes when the referee failed to award a penalty after Michael Morrison appeared to trip Chris Taylor inside the box.
On 72 minutes, City had David Martin to thank when he managed to cling on to a fiercely struck shot from Lee Hughes.
And at the death, Oldham almost snatched it but were denied when David Martin made an instinctive block from Reuben Hazell's close-range header.