The Birds beat the Brazilians 6-5 on aggregate in the two legs of the MTN8 semi-final in August, and then took a deserved three points from this League encounter.
Downs have lost four of their last five matches in the Premiership, and have scored just three goals so far.
Swallows surged ahead as early as the seventh minute as Chabangu once again haunted his former team: the attacker beat goalkeeper Wayne Sandilands to a through ball from Katlego Mashego to poke home his third goal against the Brazilians this season (having netted twice against them in the MTN8).
Sundowns came close to drawing level on the 20-minute mark through Hlompho Kekana, but Greg Etafia kept out the midfielder's fierce shot and was then relieved to watch Tebogo Langerman miss out on the rebound.
Kekana threatened again from a free-kick on 29 minutes, but Etafia was equal to the task and palmed the ball over the crossbar for a corner.
Set-pieces and long-range attempts seemed the Brazilians' best hope of a goal in the first half, as their general play lacked rhythm and penetration.
Swallows extended their advantage in the 33rd minute thanks to a brilliant goal from winger Obada, who fired home a long range shot that went in off the underside of the crossbar and gave Sandilands no chance whatsoever.
Sundowns opted for a change at half-time, replacing Elias Pelembe with Nyasha Mushekwi, but they almost went further behind within the first minute after the restart after a rare mistake from Sandilands that gifted the ball to Mashego, but the striker was unable to capitalise.
On 57 minutes the Birds almost scored through another long range screamer. This time it was captain Lefa Tsutsulupa who let fly from 20-plus metres out, but his effort rebounded off the crossbar.
Downs also found the woodwork, as Eleazar Rodgers' looping header hit the top of the crossbar before bouncing out for a goal-kick in the 70th minute. It was one of the few instances in which the tall striker was given decent service from out wide.
Substitute Edward Manqele also rattled the bar, on 78 minutes, turning inside his marker in the penalty area before firing off a left-footed effort was beyond the reach of Etafia.
In the end Sundowns lacked the necessary spirit to fight their way back into the game and the Birds were able to see out the dying minutes in relative comfort, picking up a win which takes them to fifth place on the table. Downs remain in 14th.