The victory has also propelled the Free State side to sixth place behind Kaizer Chiefs, Chippa United and arch-rivals Bloemfontein Celtic on goal difference.
The home side created the better goal-scoring opportunities in the opening exchanges with Sinethemba Jantjie causing a number of problems.
Stars broke the deadlock on 25 minutes when Siphelele Mthembu turned home Patrick Phungwayo's cross from the left flank.
The home side were in control in the first half, but they failed to add to their one-goal advantage before the break.
Following the arrival of Reneilwe Letsholonyane at the start of the second half, SuperSport upped their tempo and managed to carve out a couple of half chances.
Stars were then reduced to 10 men on 65 minutes when Phungwayo was shown a straight red card for a dangerous challenge.
Eric Tinkler's charges threw numbers forward in an attempt to bag an equaliser and they went close in the 81st minute when Sifiso Myeni's shot was superbly turned away by Robert Sangare.
Nevertheless, Stars managed to hold on to claim a valuable win against the MTN8 champions.
Next for the Free State side is another home match against Orlando Pirates on Saturday evening, whilst Tinkler's men take on Baroka FC at the Peter Mokaba Stadium on Sunday afternoon.