Stars were by far the better side in the first half, and created the first chance of the game in the 23rd minute when Luis Renteria saw his goalbound shot tipped around the post for a corner by Ezenkosi keeper Avril Phali.
George Mofokeng should have handed the hosts the lead from the resulting corner, taken by Tshepo Ramokala, but his header flew well wide of goal.
Phumudzo Manenzhe sent an effort wide in the 28th minute, as Stars continued to pile on the pressure, but they were unable to penetrate the Cosmos defence.
The score remained 0-0 at the break.
Cosmos looked much better in the second half and almost broke the deadlock in the 57th minute when Thapelo Tshilo hit the post with a diving header after Morgan Gould headed a corner back across the face of goal.
The was cause of concern for Stars in the 71st minute when George Mofokeng and Joseph Mkalipa remained on the ground following a clash of heads, fortunately both players able to continue the game after receiving treatment.
However, on a fiercely hot afternoon in Rustenburg that saw referee Jonas Nhlapo call for a water break with just over ten minutes to play, neither team managed to stamp their authority on the match.
The draw sees Stars move level with eighth-placed Bloemfontein Celtic on 25 points, although the northern team stays in ninth on goal difference. Cosmos remain second from bottom on 16 points, two ahead of basement club Black Leopards.