Oldham were reduced to 10 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 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 Windass, 39, who did well again close to the end when he beat away yet another Fryatt shot.
Oldham 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.
Oldham almost snatched it at the death but were denied when David Martin made an instinctive block from Reuben Hazell's close-range header.
Walsall needed a late goal to earn a point at Hartlepool United, despite taking an early lead through Troy Deeney.
Te home team got a helping hand on 36 minutes when Matty Robson crossed low from the left and defender Anthony Gerrard sliced his clearance into the roof of his own net after trapping the ball almost on the goal-line.
After a slow start to the second half, Hartlepool took the lead on 64 minutes when top scorer Joel Porter slid his shot home after an awful goal-kick from Clayton Ince landed at his feet.
The Saddlers levelled with eight minutes left, Alex Nicholls crossing high from the right for Sam Williams, on loan from Aston Villa, to head in from close range
Play-off chasing Tranmere Rovers struggled against lowly Leyton Orient at Prenton Park and had to settle for a goalless draw.The visitors, under new manager Geraint Williams, put in a dogged performance and fully deserved their point.