Amakhosi have now drawn three consecutive league matches and taken just two points from their last three outings, leaving Fernando Da Cruz's side fourth in the standings. They remain unbeaten this season but will be eager to rediscover their winning form when they travel to Zambia to face Red Arrows in the CAF Confederation Cup on Saturday.
Stellenbosch, meanwhile, extended their unbeaten run to four matches to move into seventh place, with Gavin Hunt's team next in action against Chippa United on October 30.
The visitors threatened first in an entertaining opening half, with Sinoxolo Kwayiba coming close to breaking the deadlock in the 21st minute. Quwan Plaatjies picked out the forward, whose right-footed effort struck the crossbar with Chiefs goalkeeper Renaldo Leaner beaten.
Chiefs gradually grew into the contest and nearly took the lead through Wandile Duba, who was denied by Sage Stephens after being played through on goal just after the half-hour mark. The Stellenbosch goalkeeper was called upon again shortly afterwards to keep out a close-range effort from Inacio Miguel.
Neither side could find a breakthrough before the interval, but the deadlock was quickly broken after the restart.
Kwayiba put Stellenbosch ahead in the 48th minute, finishing from close range after Terrence Mashego delivered an excellent cross from the left. The Mamelodi Sundowns loanee, who went on to earn the Man of the Match award, played a key role in giving the visitors the advantage.
Chiefs responded well and restored parity in the 57th minute. Reeve Frosler sent a ball over the top for Mduduzi Shabalala, who controlled it before getting past Siviwe Nkwali and beating Stephens at the near post to register his second goal of the season.
The hosts pushed for a winner as the match opened up, with both coaches turning to their benches in search of a decisive moment. Flavio Da Silva returned to action for Chiefs after a two-month absence, while Stellenbosch introduced veteran striker Bradley Grobler.
Chiefs came close to completing the turnaround when Asanele Velebayi tested Stephens with a powerful effort, but the goalkeeper produced another important save.
Despite late pressure from both sides, neither could find the winning goal, leaving Amakhosi frustrated at home while Stellenbosch took a valuable point back to the Cape.
Chiefs will now turn their attention to their continental campaign against Red Arrows, while Stellenbosch have a longer break before their next league assignment against Chippa United.