Ezenkosi remain seven points from safety with four matches remaining, and having won just two games all season must improve if they are to save themselves.
Stars were always in control of this one, with Patrick Malokase netting a brace, and Themba Ntumi and Sibusiso Msomi also on the scoresheet. Robert Tomanyane netted a late consolation for Cosmos.
The game finished on a sour note when both sides were reduced to 10 men in the second half, Malokase getting his marching orders along with Cosmos' Ousmane Berthe.
Malokase opened the scoring with a fine solo effort as he ran through the Cosmos defence to score, before adding a second with a header from Vuyo Mere's corner.
Jackson Mabokgwane saved well from Bamuza Sono and Siyabonga Nontshinga either side of half-time, before Malokase was then shown a straight red by referee Lwandile Mfiki for a crude two-footed lunge on Vincent Kobola, which can leave him with no complaints. With just two matches remaining in the campaign, it means his season is over.
Cosmos continued to press and now with a numerical advantage were creating more chances.
Their pressure finally paid off when Tomanyane collected a pass from Nontshinga and scored from six yards.
The comeback was short-lived though, as Berthe fouled Joseph Molangoane in the area and received his marching orders, with Ntumba converting the resultant spot-kick.
Stars added a fourth deep into injury-time when Msomi smashed the ball home from the edge of the box.