The match got off to an exciting start, with the teams looking determined to attack from the word go on the night.
In the 16th minute, Sundowns captain Ramahlwe Mphahlele tried his luck from range from the right-hand side, but his effort went wide of the target.
Chippa goalkeeper Daniel Akpeyi was called into action in the 26th minute when he gathered Teko Modise's attempt from a free-kick with ease.
Themba Zwane was set through on goal by Sundowns' creative midfielder Modise three minutes after the half-hour mark, but he was ruled offside.
Nigerian goalkeeper Akpeyi denied Sundowns forward Mogakolodi Ngele ten minutes before the interval, who had let rip from 30-yards out.
The Brazilians continued to pressure the Chilli Boys for the opening goal. In the 51st minute, Tebogo Langerman's dangerous cross was cleared by James Okwuosa.
The pressure finally paid off in the 68th minute when Anthony Laffor's shot was deflected into the back of the net off Diamond Thopola, much to the delight of the Sundowns fans.
With nine minutes left on the clock, Chippa midfielder Lerato Chabangu beat his marker before forcing Sundowns goalkeeper Denis Onyango into a good save.
The match ended 1-0 in favour of Sundowns, while Chippa returned to losing ways in the League.