Lidoda Duvha were targeting a win that would have seen them move back into second position on the log standings but, having been in third coming into the encounter, found themselves slip behind Stellenbosch by virtue of an inferior goal difference.
With the game level at the break it was Cosmos who grabbed the lead through Linda Mntambo who fired home via a rebound.
The advantage was doubled by Nkanyiso Madonsela with previous goalscorer Mntambo providing the assist.
Into stoppage time Leopards were handed a lifeline as Shane Thompson was sent off for a hand ball and the visitors were given a penalty.
However, Siphelele Mkhulise wasn't able to convert the spot kick and Leopards remain a single point behind second-place AmaZulu.