Sundowns skipper Hlompho Kekana decided matters with a glancing header in the 83rd minute following a free-kick into the box from substitute Teko Modise.
The victory leaves Pitso Mosimane's side in fourth place on the table with 44 points from 22 fixtures - two points shy of leaders Cape Town City, and one behind Bidvest Wits and Kaizer Chiefs.
Downs and Wits have two games in hand on the Citizens and Chiefs, while SuperSport are now six points adrift of the summit.
The Brazilians, who won the reverse fixture 5-0 last week, started the rematch brightly, as Khama Billiat flashed a strike narrowly wide after linking up with fellow attacker Percy Tau in the opening minute.
Kekana threatened midway through the first stanza with a useful free-kick, but Ronwen Williams tipped the effort over the crossbar.
SuperSport nearly stole ahead just before the break via Clayton Daniels, but the defender's shot from inside the box was blocked by an alert Denis Onyango.
Onyango was called into action again 10 minutes after the restart, as he dropped down smartly to gather a long-range attempt from Reneilwe Letsholonyane.
United suffered a setback in the 67th minute, as striker Kingston Nkhatha was stretchered off with an injury prompting the introduction of winger Thuso Phala.
Kekana then rose at the death to snipe the spoils for the Absa Premiership champions off a telling delivery from Modise, who came on for Mzikayise Mashaba in the 61st minute.