Nduduzo Sibiya scored the only goal of the game in the second half as Golden Arrows stunned their hosts and deservedly won a place in the quarterfinals.
It means Sundowns have now won two of their last nine matches, a run that has seen them slip in their challenge for the Absa Premiership this season as well.
Sundowns made the bright start and Billiat might have done better after he danced into the Arrows penalty box, but delayed the shot and in the end visiting keeper Nkosi Gumede was able to make the block.
But Arrows grew into the game as the half wore on and Sibusiso Sibeko had two excellent chances to score.
The first saw him steer the ball wide at the back post, and with the second he headed over the bar when he had a free sight of goal in the six-yard box.
Sundowns huffed and puffed in the second period and had a few clear-cut chances.
Hlompho Kekana shot wide when well-placed, while Billiat had a header at the back-post, but could not hit the target.
And the decisive moment of the match came on 66 minutes when Sibiya raced clear on goal after a clever flick past Motjeka Madisha. He kept his composure and beat Mweene with a low shot into the corner.