Arrows stunned the Brazilians via goals from Mabhuti Khenyeza and new signing Ryan Chapman at Chatsworth Stadium.
Substitute Themba Zwane scored for Downs, who had Bafana Bafana midfielder Bongani Zungu sent off for a second bookable offence in the 17th minute.
Experienced striker Khenyeza gave the hosts a seventh minute lead from the spot after he was tripped by goalkeeper Denis Onyango in the box.
In the eighth minute Philani Zikalala made a double save to deny Khama Billiat as Sundowns, who showcased new Ivorian signing Bangaly Soumahoro, pressed forward.
Downs, however, soon suffered a setback when Zungu was given his marching orders.
In the 45th minute Onyango denied Gladwin Shitolo an opportunity to double the score as he made a good save to his right.
In the second half, Zwane made an immediate impact as he equalised moments after replacing Cuthbert Malajila at the break.
Chapman, who had come in for Andile Fikizolo, almost scored with his first touch as well, but his strike from range went over the crossbar
Chapman, though, was rewarded when he pounced in the 70th minute to snare the spoils.