The encounter had ended 1-1 after 120 minutes after Rendani Ndou cancelled out Tshegofatso Mabaso's strike, forcing the clash into a penalty shoot-out.
Siwelele threatened on counter-attacks in the opening 10 minutes with Kabelo Mahlasela proving to be a handful on the left wing.
Roggert Nyundu could not take a glorious opportunity to get on the scoresheet in the 16th minute after some brilliant work from Ndumiso Mabena, who delivered a low squared pass inside the box but Nyundu tripped himself while in the position to tap into the back of the net.
Walter Musona brought the best out of Patrick Tignyemb in the 30th minute with a pile driver from outside the box.
The match started to become physical and fierce after 40 minutes with both sides not pulling away from challenges.
The first stanza ended goalless with both sides struggling with the final pass in the final third.
Rodney Ramagalela nearly broke the deadlock in the 56th minute but his low strike from the edge box went across the face of goal by a few inches.
Mahlasela should have grabbed the lead for Veselin Jelusic's charges in the 65th minute after going through on goal on the edge of the box but goalkeeper George Chigova came out of his line in time to block the move.
Rendani Ndou made a brilliant run on the left side of the box to go through on goal in the 73rd minute but his left footed shot could not find the target.
Jabulani Maluleke thought he had found the back of the net 10 minutes from time with an inch-perfect free-kick from the edge of the box but Tignyemb produced a great reflex save to clip the strike out of the top left corner.
There was end-to-end attacks after 85 minutes with both sides looking for the winner.
Molekwa brought in Puleng Tlolane in the last minute replacing Musona while Jelusic threw in Tshegofatso Mabaso in place of Mahlasela with extra-time imminent.
The match eventually went into extra-time after both sides could not find the back of the net, logged at 0-0.
Mabaso finally broke the deadlock in the stroke of the first half of extra-time following a clever free-kick where Mabena picked him out in the area and he turned brilliantly to hit a low shot into the bottom corner.
Ndou levelled matters for City six minutes before two hours with a header from the near post following a great delivery from Maluleke through a corner kick.
The was match forced into a penalty shoot-out, where Celtic held their nerve to triumph 4-3 to advance to the final.
Celtic will now face Bidvest Wits in the final, which is scheduled to take place at the Princess Magogo Stadium on Saturday, 2 December at 18h00.