The draw sees the Chilli Boys move to seventh place on the league standings, while the Clever Boys remain 15th on the table.
The Clever Boys were oozing with confidence having secured a 2-0 victory over SuperSport United at home in a league game in midweek.
Lehlohonolo Majoro started upfront as a sole striker as Gavin Hunt had to do without James Keene and Bongani Khumalo, who both scored against SuperSport.
On the other hand, the Chilli Boys were also eyeing their second consecutive league win having defeated AmaZulu 2-0 at home last weekend.
Linda Mntambo, who netted twice against AmaZulu, started behind the main striker Mxolisi Macuphu for Teboho Moloi's side.
Wits were the better side in the opening exchanges, but the Chippa defence which was led by Nigeria international James Okwuosa looked solid.
However, as the match progressed, the Clever Boys began penetrating the Chilli Boys defence and they managed to break the deadlock.
Vincent Pule was the man, who fired past Chippa goalkeeper Daniel Akpeyi to make it 1-0 to Wits - silencing the home crowd in the process.
The Chilli Boys pushed forward in numbers in search of the equalizing goal, but they were struggling to unlock the experienced Clever Boys defence.
The score was 1-0 to Wits at half-time following a tightly contested first half in the city of Port Elizabeth.
Moloi made a change a few minutes into second-half - pulling out Bantu Mzwakali and he introduced Thabo Rakhale as the hosts looked to level matters.
The home side piled pressure on the Wits defence which was forced to concede free-kicks with tough-tackling Edwin Gyimah collecting a yellow card.
Pressure mounted on the visitors' defence and they finally concended with 10 minutes left on the clock much to the delight of the home crowd.
Kristopher Bergman beat Wits shot-stopper Darren Keet to make it 1-1 following some good work by former Jomo Cosmos forward Macuphu.
Wits then pushed for a late winning goal, but Chippa stood firm at the back and ultimately, the match ended in a 1-1 draw.