While Sundowns had more possession in the first half they still went into the half-time break trailing by a goal from Welcome Qalanto.
The Brazilians were able to find an equaliser through Wayne Arendse midway through the second half, but were unable to push on for the win.
Sundowns played some beautiful passing football, but they lacked that final killer pass that would unlock the Chippa defence. Instead, their next first chance on goal came from a 35-yard free-kick in the 14th minute.
Esrom Nyandoro let fly with a powerful shot that looked destined for the top corner, but it went inches wide of the target with the keeper well beaten.
Chippa had produced hardly any play in the Sundowns half and it was very much against the run of play when they took the lead in the 30th minute through Qalanto’s sixth goal of the season.
The Chilli Boys' attacker rose highest to head home a free-kick from six-yards out into the bottom corner.
The second half saw the away side pick up where they left off – firmly in control of the match, but still unable to find the back of the net.
In the 67th minute second half substitute Teko Modise did come close to finding the equaliser, but he saw his 25-yard thunderbolt strike the woodwork and bounce away from danger.
Two minutes later, however, Downs did find the equaliser through Arendse, who rose highest to head home a corner kick.
Try as they may, Downs could not find a winner as the sides had to settle for a share of the spoils.