Sundowns opened the scoring via Cuthbert Malajila in the 30th minute, but Sangweni equalised with a curling free-kick against his former side on the hour-mark at Nelson Mandela Bay Stadium.
Sangweni was given his marching orders with four minutes to go after receiving a second caution for holding back Tebogo Langerman.
The Brazilians started positively and applied pressure form the word go – they finally made it count when a mistake in the Chippa defence allowed Khama Billiat to steal the ball and unselfishly square for Malajila who scored into an empty net, 1-0.
The visitors could not add to their goal tally and were made to pay in the second half after a spirited performance from Chippa United.
The home side began seeing more of the ball in the second 45 and found their reward with the equaliser in the 60th minute courtesy of a Sangweni strike, 1-1.
Downs tried to find a winner after that, but the closest they came was a Mario Booysen header in the 80th minute that was well-saved by the keeper.
Despite earning a share of the spoils, the night did end on a rather sour note for Chippa following the dismissal of Sangweni, who picked up an automatic two-match ban.
The draw is Sundowns' third of the season and sees them stuck in fourth place on the log with 15 points from their nine games, a staggering 10 points adrift of current league leaders Kaizer Chiefs, who drew 1-1 with Moroka Swallows in a simultaneous fixture.
Chippa, on the other hand, despite many expecting them to struggle this season are up to eighth on the table with 14 points, only three points adrift of second-placed Ajax Cape Town.