The Zambian international has become something of a penalty taker and proved his reliability once more, scoring in the 80th minute.
The spot-kick was awarded when Mzikayise Mashaba went down inside the area after a challenge from Ezenkosi defender Themba Shabalala.
On the bumpy Goble Park field, both sides struggled to put their foot on the ball and pass it around in the first half.
Aleni Lebyane got into a good position inside five minutes, but could not get a proper touch inside the six-yard area.
Just before the break Noah Chivuta attempted to cross the ball instead of shooting, which was not the wisest decision, and Lebyane sent a header just wide a few moments later.
In the second half Zimbabwean Taongo Dondo had a shot, but it flew over the bar and never troubled Mweene.
In the final 15 minutes of the game, Stars’ new signing from Togo, Ouro Sedata, headed an opportunity wide following Diego Brown’s corner kick.
Stars applied some more pressure in the closing stages with Edward Mnqele and Mashaba sending efforts just wide.
Then it was time for Mweene to make the difference, sending his spot-kick into the back of the net to the delight of the home fans.
Former South African Under-23 international Thapelo Tshilo made a return to Cosmos for the match, having rejoined the club from Mamelodi Sundowns where he was seeing little action.