Striker Corr came on 14 minutes from time after the Wiltshire side had gone 2-0 down to promotion-chasing Leicester.
The hit-man swivelled and volleyed the ball into the roof of the net after the Leicester rearguard had failed to clear a corner.
Swindon started the game brighter and an Anthony McNamee corner was headed just wide of the right-hand post by Lee Peacock within the first two minutes.
Leicester captain Matty Oakley struck back for his side five minutes later with a fine solo run that was only stopped by Swindon goalkeeper Phil Smith diving to save at his feet.
In the 28th minute Patrick Kanyuka was booked for unsporting behaviour when he handled the ball into the net from a McNamee cross.
Leicester's top-scorer, Matt Fryatt, set up Oakley just before the break but his shot was saved by Smith.
Leicester took the lead 12 minutes after the break and it was their captain they had to thank for it.
Oakley picked up the ball 25 yards from goal and beat off two challenges before firing the ball into the roof of the net.
Fryatt doubled Leicester's advantage 17 minutes later after Swindon goalkeeper Smith made a hash of an attempted clearance.
Fryatt picked up the loose ball before rounding the hapless goalkeeper and slotting the ball home.
Corr came on in the 76th minute and eight minutes later Swindon were handed a lifeline when Peacock crossed to Cox who finished from two yards out - his 15th goal of the season.
Swindon equalised just before the death with Corr's first goal of the campaign.
The lanky hit-man pounced after Leicester failed to clear a corner and fired the ball into the roof of the net from ten yards for a priceless point at the club which sacked Maurice Malpas on Friday.