Nontshinga cancelled out Joseph Obaje's early goal in the bottom-of-the-table clash at Giyani Stadium.
The draw does not create any daylight between Cosmos in last position and Leopards in 15th, as both clubs remain in the relegation zone.
The opening goal came after just 16 minutes when Leopards' Nigerian striker Obaje buried his shot from close range following a cross from the left wing by Mahlatse Maake.
But Cosmos responded well, never giving up, and were rewarded in the dying seconds of regulation time when Nontshinga netted from close range following an assist by Bongani Theletsane.
The Obaje goal gave life to Leopards who started playing with a real buzz and the Nigerian forward was evidently lifted as he continued asking questions of Cosmos’ Ousmane Berthe and Themba Shabalala.
For the remainder of the half, Leopards’ goal scorer and assist maker Obaje and Maake, came under some heavy challenges from Cosmos.
Sono and Berthe put in some big tackles to try and nullify the men who had put the home side ahead, but it did not deter Leopards who kept fighting and held their lead until the half time break.
It took until the 43rd minute for the next genuine attempt on goal and Cosmos can thank goalkeeper Avril Phali for making a brilliant save to deny Samuel Mabunda from giving Leopards a 2-0 lead.
The second half started with a bang as both sides began running hard at each other; Leopards in search of a second goal and Cosmos in search of an equaliser.
Maake, a victim of some rough challenges in the opening half, was booked for a foul on Cosmos centre back Shabalala as he attempted to stand up for himself in a few strong tackles.
Then in the 58th minute Jomo Sono made two tactical changes, bringing on Alton Meiring and Bongani Theletsane to add some experience and some pace to the attack respectively.
But it was Lidoda Duvha who fashioned the next attempt on bar when Thabo Mongalo’s right footed shot from distance sailed over the crossbar.
Meiring drew a save from Posnett Omony on 68 minutes when his header from Sono’s corner kick was tipped around the post by the big Ugandan keeper.
In the 79th minute Omony is called into action again, this time denying Wambi and Moloto in quick succession and it seemed as if Leopards would take the full points.
But Omony could do nothing to deny Nontshinga his 90th minute equaliser.