Cosmos therefore remain in 15th place with 17 points from 21 games while Stars remain in 3rd place with 35 points.
"We are happy with the point, it's better than nothing coming here to face a team like Cosmos," said Stars skipper Duncan Lechesa.
"It was not an easy game as they are fighting off relegation and they came hard at us. We were unlucky to lose a player but we showed character and fought hard with 10 men for this point, so we are happy."
Stars had the better chances but good goalkeeping by Cosmos keeper Avril Phali denied them victory while his counterpart Kennedy Mweene also made timely saves to earn his team a valuable point.
It was all Stars in the first half. In the 10th minute Moses Mbuyane shot straight at goal but Phali put his foot out to deny the nippy striker a goal. Six minutes later Mbuyane was again on the edge of the area but this time his rocket deflected off a Cosmos defender.
With less than 10 minutes to go Stars went up in numbers for their third corner of the match. The ball kindly fell to the feet of Sthembiso Ngcobo who hit it hard but just inches past Phali's upright.
Stars defender Sipho Nkosi got a second yellow card for a foul five minutes before halftime and this gave Cosmos room to attack.
Although they camped in Stars half Reneilwe Letsholonyane and Nkosinathi Nhleko both missed good chances to put Ezenkosi in the lead before the break.
Cosmos started the second half like they ended the first but their early pressure got them nothing as Stars took off striker Kingston Nkhatha and replaced him with defender Christopher Tsotsetsi.
Despite being one-man short Stars still got forward to test Phali. Ngcobo left his marker for dead on the left wing and picked Mbuyane out in the box. The latter dallied with the ball and gave the back-peddling Cosmos defenders enough time to get back and deflect his goal-bound shot.
In the 80th minute Mbuyane beat Phali from outside the box with a blistering shot but the goal was invalid as two Stars players were in an offside position. A minute later Diyo Sibisi headed the ball inches wide of Phali's upright.