The only goal was scored by Fanyana Dhladhla.
The game was fairly even possession wise with very few scoring opportunities, the better chances fell for the home side but to their credit Cosmos defended well.
After Stars scored Cosmos did throw everything into attack but Stars defended well and try as they might Cosmos never looked like cracking the Stars defence.
Sthembiso Ngcobo nearly gave Stars the lead in the 61st minute when his shot went narrowly past the upright.
The goal came was scored in the 70th minute when the ball kicked high down field for Ngcobo to head it onto Dhladhla who scored with a close-range shot giving keeper Avril Phali no chance.
Cosmos almost came up with an immediate reply, but keeper Kennedy Mweene kept out Lucky Mhlathe’s volley with a fine diving save.
Stars held off a late onslaught from the visitors to secure their victory and a place alongside Bloemfontein Celtic and Mamelodi Sundowns in the semifinals.
Supersport United and Kaizer Chiefs will contest the final berth on Sunday afternoon at Loftus.