The match continued on from the 42nd minute on Wednesday morning, after the encounter was abandoned on Tuesday evening, following a power failure at the stadium.
The Brazilians had started the clash the brighter of the two sides, with Percy Tau and Yannick Zakri causing a few problems in the final third.
Sundowns' best and only chance arrived after 20 minutes when Hlompho Kekana sent a header straight Chippa goalkeeper, Daniel Akpeyi, who managed stop the ball from crossing the line at a second attempt.
Chippa, meanwhile, certainly held their own and did not allow Sundowns to completely take over the encounter, although they could only force Wayne Sandilands into one save in the opening 45 minutes.
Chances were hard to come by in the opening exchanges of the second half, although Akpeyi was kept busy by in-coming crosses, while Sandilands was a spectator.
Dan Malesela opted for a change after 65 minutes as Tshwarelo Bereng replace Mbulelo Wambi.
With Sundowns struggling to break down the Chippa defence, Pitso Mosimane opted for a double change as Zakri and Themba Zwane made way for Leonardo Castro and Teko Modise.
Castro nearly made the perfect impact two minutes after his arrival, but Akpeyi did well to keep out the Colombian's left-footed effort.
The home side were camped in the Chippa half in the closing stages, forcing Malesela to withdraw Lerato Manzini for defender, Mpho Mvelase.
However, Chippa managed to see off the late surge from Sundowns and claimed a point, which Sundowns remain fourth, while Chippa move one point clear of Orlando Pirates in ninth.