Kagisho Dikgacoi and Joseph Musonda also netted for Abafana Bes’thende, while Dario Monteiro and Katlego Mphela scored for the Brazilians, who saw Shere Lekgothoane sent for an early shower.
Arrows got off to the perfect start when skipper Dikgacoi opened their account in the seventh minute with a low right-footed shot following a good pass by Doctor Sangweni.
Dikgacoi then turned provider in the 27th minute as Arrows extended their lead via a close-range strike by Musonda.
Sundowns pulled one back 12 minutes later when Monteiro scored from inside the area after collecting a pass by Kurt Lentjies.
The score remained 2-1 at the break and Arrows continued their dominance in the second half.
Sundowns were reduced to 10 men in the 51st minute following Lekgothoane’s professional foul on Abia Nale.
Substitute Richard Henyekane made it 3-1 to Arrows in the 77th minute when he slotted home from a corner, but the Brazilians reduced the deficit two minutes later through substitute Mphela, who headed home a cross by fellow substitute Dillon Sheppard.
However, Arrows again restored their two-goal cushion in the 87th minute when Henyekane slotted home from inside the area, to put the result beyond doubt.