The Citizens had drawn first blood in the 22nd minute when Mduduzi Mdantsane netted his first goal for the club since arriving from Baroka FC midway through last season.
The goal followed a mistake by keeper Veli Mothwa, who gave the ball away to Craig Martin who in turn cut it back for Mdantsane to score with a composed finish from about 10 metres out.
Chippa nearly managed a spectacular equaliser in first-half added time, but Frederic Nsabiyumva's overhead kick was superbly saved by home keeper Peter Leeuwenburgh.
The Chilli Boys kept pressing for a goal after the restart and they had their reward in the 53rd minute when Chidi Kwem finished neatly.
Sniffing blood the visitors continued to attack and were unlucky not to get a winner as Isaac Nhlapo's cross-cum-shot struck the woodwork in the 67th minute before debutant Bienvenu Eva Nga's effort was cleared off the line by Thato Mokeke 10 minutes from time.
Meanwhile, Mokeke's former club SuperSport United were involved in another Premier Soccer League match on Saturday night, against Black Leopards at the Lucas Moripe Stadium.
It proved to be a marathon encounter - after just nine minutes of action, the game was halted for around an hour as a lightning storm together with very strong wind and rain made conditions too dangerous to continue.
When the match resumed, it was Matsatsantsa who shocked Leopards with a 24th-minute goal, thanks to a quality finish by Bradley Grobler, following an assist by Jamie Webber.
Lidoda Duvha also had their moments in front of goal though it was the hosts who nearly scored again when Tebogo Mokoena hit the crossbar three minutes before the interval.
After the break, Leopards piled the pressure on the SuperSport defence as they searched for an equaliser and the home team's task got even harder when Onismor Bhasera was sent off on the hour mark after getting a second yellow card.
The Limpopo side kept on coming at Matsatsantsa, but some resolute defending and brave goalkeeping by Ronwen Williams enabled the Tshwane club to maintain their lead before Grobler completed his brace in the final minute of added time.