Despite going behind and then having a penalty saved, Amakhosi prevailed after Knowledge Musona’s late equaliser, and a fantastic performance from 'Spiderkid' during the shoot-out.
Siphiwe Tshabalala made a return to the pitch after an adductor muscle injury kept him out for the last three weeks.
Steve Komphela left Bafana Bafana midfielder Luyolo Nomandela on the bench, choosing to start with Camaldine Abraw and Abdul Basit Adam up front.
Abraw hit the post from a corner kick early on, while Musona and Willard Katsande went close for Chiefs as both sides started brightly.
Ea Lla Koto kept George Lebese and Tshabalala quiet in the first half, while Danny Venter and Adam caused problems for Amakhosi.
In fact, Adam should have put Stars ahead on half an hour, when he blasted over the bar from point blank range.
Chiefs dominated possession as the second half got underway, but could not find a way through on goal.
On the hour mark Lebese came close to opening the scoring, when Daniel Agyei – who had looked out of sorts all afternoon – failed to collect Parker’s corner-kick.
Lebese was on hand to pounce on the loose ball, but his shot hit the post.
On 68 minutes Musona was brought down in the box by Sibusiso Mthethwa, and the referee pointed to the spot.
However, Agyei’s fortunes changed and he saved Parker’s spot-kick.
The Bafana Bafana striker earned a yellow card as he attempted to hit home the rebound but caught the keeper instead.
Ea Lla Koto were awarded a penalty just minutes later, after Katsand’s reclkess challenge on Venter.
Akoriko sent Khune the wrong way to make it 1-0.
Parker attempted to atone for his sins 10 minutes from time, trying a shot from long range that went close, but ultimately only troubled the crossbar.
With three minutes on the clock, Siboniso Gaxa found Musona with a pin-point cross, and the Zimbabwean hit-man nodded home from close range.
Extra-time was a dull affair, with both teams practising caution, and the match ended 1-1.
Amakhosi dominated the shoot-out, scoring on all four attemps, while Khune saved Stars’ first two spot-kicks.
Chiefs join Platinum Stars and SuperSport United in the semi-finals.
Mashego: Saved, Yeye: Scored
Ouro-Akoriko: Saved, Katsande: Scored
Bobe: Scored, Dladla: Scored
Masehe: Scored, Parker: Scored