The Chloorkop outfit had to weather a late storm after Supersport's Katlego Mashego pulled a goal back with 20 minutes to play, but Trott Moloto's men held out to ensure that they will be in the hat when the draw for the next round is made.
Driving rain in Rustenburg had made the pitch difficult to play on for two teams who generally favour an attacking approach based on passing and possession.
Supersport were forced into an early change when Letladi Madubanya picked up an injury in a crunching challenge with Johannes. Playmaker Sibusiso Mahlangu was an able replacement but his particular skills were not suited to the difficult conditions.
Downs created the first scoring chance in the 20th minute, with Esrom Nyandoro shooting over from the edge of the penalty area after good work down the right flank by Fanyana Dhladhla.
But Supersport almost took the lead less than a minute later. Daine Klate scampered free down the left, drew goalkeeper Calvin Marlin off his line and squared for Kermit Erasmus, but Johannes made an impressive block to keep out the youngster's goal-bound effort.
The heavy pitch looked as if it would have a high rate of attrition, and it claimed its first victim when Dhladhla had to limp off in the 36th minute, replaced by his namesake Josta Dladla.
Lerato Chabangu struck a curling shot just wide of the post in the 44th minute and a minute later he sent Godfrey Sapula through on goal, but the veteran midfielder could only poke his shot the wrong side of the upright under pressure from goalkeeper Denis Onyango.
Sundowns took the lead four minutes after half time, with Moriri sneaking in between Bongani Khumalo and Onyango to lob the ball into the back of the net after neither United player took the responsibility of dealing with Michael Manzini's long ball out of defence.
Johannes then doubled the Brazilians' advantage in the 58th minute thanks to some poor goalkeeping from Onyango, who allowed the defender's powerful shot from the corner of the penalty area to burst through his hands and travel into the top corner.
Matsatsantsa halved the deficit 10 minutes later through a stunning free kick from substitute Mashego. The striker curled his shot over the wall and the ball clipped the inside of Marlin's left hand upright before travelling over the goal line.
Supersport resorted to long balls forward in an attempt to unsettle Sundowns' defence, but they found Marlin an immovable object. The former United keeper made two fine saves in the last ten minutes of regulation time to deny Fikru Tefera and Denis Masina.
Not that Matsatsantsa didn't have their own chances on the break: substitute Bryan Aldave twice missed out on good scoring opportunities as the hosts left big gaps at the back in the dying minutes.
In injury time United were reduced to 10 men as Onyango sprinted off his line and felled Dladla, who had run clean through on goal. September pulled on the goalkeeper's jersey but the final whistle was blown just a few moments later.