The game, which was abandoned last night due to a power failure in the area, resumed at 10h00 in the 42nd minute with the teams unable to score before the break.
Downs were the brighter side on Tuesday with Hlompho Kekana coming closest to a goal when his bullet header struck Chippa goalkeeper Daniel Akpeyi without the Nigerian knowing much about it. Half a metre either side and it would have been a goal.
Wayne Sandilands in the Sundowns goal did make one fine save from an Andile Mbenyane effort, but was largely untested in the first 42 minutes.
The match resumed with the remaining three minutes of the first half, during which little was done by either side as they went into the tunnel with the scoreline unchanged.
The second half restarted at a sluggish pace, with Sundowns controlling possession in the attacking half, but were unable to threaten Akpeyi in the Chippa goal.
The hosts' best chance of the half came from substitute Leonardo Castro in the 78th minute, when he broke into the Chippa area and sent a low shot towards goal from an acute angle but Akpeyi was up to the challenge.
Two minutes later the Chilli Boys finally brought a largely inactive Sandilands into play as Diamond Thapola unleashed an effort from range, but the 'Downs stopper palmed the ball to safety.
There were shouts for a penalty late on as Castro went down under a challenge from Christopher Bergman, but the referee waved it off as he pointed for a goalkick.
The point sees The Brazilians remain in fifth place with 33 points from 15 games, trailing leaders SuperSport United by two points with three games in hand.
Meanwhile, Chippa remain outside the top eight in ninth spot with 22 points from 19 games, and trail eighth-placed Maritzburg United by a point.