The Brazilians opened the scoring through Dove Wome but Mogakolodi Ngele equalised from the penalty spot before Mduduzi Nyanda scored the winner in the second half at Moruleng Stadium.
The match kicked off 30 minutes later than scheduled due to bad weather.
Earlier, Matsatsantsa defeated Moroka Swallows 3-1 in their respective last-eight duel.
Sundowns showed their intentions as early as the first minute with Anthony Laffor firing a snapshot wide of goal before forcing Siyabonga Mpontshane to make a low save 10 minutes later.
Pitso Mosimane’s men took the lead in the 13th minute as Mpontshane was left wrong-footed on the line by a deflected strike from Wome following a quick attacking move.
Downs captain Alje Schut then saw his header going over the crossbar in the 15th minute, before Tebogo Langerman fired over a minute later.
Nyanda came close to finding the equaliser in the 24th minute with a brilliant curled effort which came off the inside of the upright with Mweene well-beaten.
Wome then tested Mpontshane from a tight angle in the 28th minute but the Stars goalkeeper was equal to the task, while Mweene also did well to stop a long range effort from Ngele a minute later.
The hosts eventually leveled matters in the 39th minute as Ngele converted calmly from the penalty spot after Siphelele Mthembu had been brought down by Mweene.
Stars came close to taking the lead in the 51st minute when Mthembu made a great run to meet a cross from Nyanda on the edge of the six-yard box, only to sidefoot wide of the upright.
Sundowns were awarded a penalty of their own five minutes later after Cuthbert Malajila had been brought down inside the box but Billiat blasted his shot over the crossbar after his first effort was saved illegally by Mpontshane.
Stars had opportunities at the other end but Mweene did well to tip Ngele’s effort over the crossbar in the 68th minute, before Robert Ng’ambi volleyed over the target a minute later.
Dikwena eventually made it count in the 70th minute when Nyanda showed his composure to control a loose ball inside the box before tucking his low shot under Mweene and into the back of the net.
Ngele almost increased the lead five minutes later when he got behind the defence on the left side of the box, but Mweene dived to his left to parry his well-struck shot wide of goal.
Despite throwing a lot of players forward in search of the equaliser, Sundowns were unable to create clear-cut chances, while Mzikayise Mashaba shot over the crossbar on the half-volley in added time.