The Brazilians appeared destined for their first league defeat of the campaign after Chippa took the lead in the 78th minute. Sirgio Kammies needed only a minute after being introduced from the bench to make an impact, finishing an opportunity created by Khaya Mfecane.
Chippa had defended resolutely throughout a contest played in rainy conditions, with the wet surface making the pitch heavy and difficult to negotiate. Stanley Nwabali was central to their resistance, producing several important interventions as Downs piled on the pressure.
Grant Kekana tested the Chippa goalkeeper with a header from Aubrey Modiba's cross in the 75th minute, but Nwabali dealt with it comfortably. Teboho Mokoena later saw another header kept out, while Cassius Mailula also went close when his cross was cleared before Iqraam Rayners could arrive.
The visitors had their moments on the break, with Figuraeido coming closest in the 69th minute after being released through on a counter. His effort was deflected away by Thapelo Morena, however, and Chippa struggled to properly trouble Ronwen Williams.
There had been little clear-cut action during the opening half, although Williams survived an awkward moment in the 32nd minute when he slipped while receiving a back pass before recovering to clear ahead of an approaching attacker.
With the sold-out crowd expecting a famous Chippa victory, Antonio van Wyk struck in the 95th minute to level the contest and deny Chippa their first-ever Betway Premiership win over Sundowns.