Joseph Mkalipa scored for Stars, while Reneilwe Letsholonyane netted for the Ezenkosi.
Platinum Stars took the lead in the 23rd minute when Mkalipa scored with a superb free-kick.
Cosmos almost drew level in the 31st minute when Dikgang Mabalane hit the side-netting from a cross by Davies Mwape.
A minute later, Simba Marumo missed a glorious opportunity to extend the visitors’ lead when he shot wide from close range, with just the keeper to beat.
The score remained 1-0 at the break.
Cosmos showed more urgency in their game in the second half and were duly rewarded two minutes after the restart when Letsholonyane scored with a low shot after collecting a cross from Tshepo Moloto.
Mabalane went close to handing Cosmos the lead when he hit the crossbar with a fierce shot in the 70th minute.
Koketso Mmotong should have handed Stars the lead in the 75th minute when he latched onto a loose ball following a goalmouth scramble, but the midfielder shot wide from close range.
That was the final chance of the match, with a draw being a fair reflection of the game.