The scores had been level at 2-2 after 120 minutes following goals from Sibusiso Vilakazi and Sthembiso Ngcobo, while Katlego Mphela and Man of the Match George Maluleka netted for Chiefs.
Coach Stuart Baxter started with an attacking line-up featuring Mphela, Bernard Parker and Kingston Nkhatha, with natural wide-men Siphiwe Tshabalala and George Lebese starting on the bench.
However, the moved looked to have backfired early on as the Students dominated Chiefs, with Ngcobo particularly influential.
Chiefs weren't helping themselves with some dodgy moments in defence. Mulomowandau Mathoho had to be sharp to prevent Asiwe Langwe a shot on goal after a misplaced back-pass, before Wits hit the woodwork – this time Parker played a poor ball back to his keeper, allowing Ngcobo to sneak in and beat Itumeleng Khune to the ball, only to see the header come back off the woodwork.
The goal did eventually come though, on 22 minutes. Vilakazi played a great one-two before attempting to chip the ball over the onrushing Khune, who brought the Wits captain down.
Khune disputed the call, but it was a clear penalty and Vilakazi made no mistake from the spot.
Chiefs almost hit back straight away when Tsepo Masilela swung in a great cross from the left, but Mphela just failed to get his diving header on target.
The Students continued to have the better of the play, with the visitors resorting to long-range efforts, but then a lifeline on 35 minutes. Maluleka showed great skill in the box to outfox Phumlani Ntshangase, who lunged in and conceded the penalty. Mphela made no mistake.
It took Wits just two minutes of the second half to reclaim the lead, with former Chiefs man Ngcobo getting the goal with a nice first-time finish after a short corner.
But Amakhosi were level again six minutes later thanks to some amateurish defending from the hosts. Chiefs managed to keep the ball alive when Wits were trying to sheppard it out, allowing Nkhatha to run on goal and set up Maluleka for the easiest of finishes.
Chiefs were playing much better now and Maluleka came close with a rasping drive from distance, though Wits almost reclaimed the lead with 12 minutes to go after some good build-up play saw Vilakazi fire off a shot, but Khune came up with a fine save.
Substitute Ryan Chapman almost won the game in regulation time when a long throw-in fell at his feet, but he dragged his shot wide.
Vilakazi’s dipping shot from distance was the closest the Students came in extra-time, while Chiefs were within inches of reaching the Final when ‘Shabba’ played a pass to Parker, but his chip hit the upright.
Josephs was brilliant in the penalty shootout, saving to deny Reneilwe Letsholonyane and Shabba, though the effort was retaken. However, the second attempt hit the upright, allowing former Chiefs man Onismor Bhasera to slot the winning penalty and send Wits through.
PENALTY SEQUENCE: Letsholonyane saved, Vilakazi scores; Tshabalala misses, Chapman scores; Parker scores, Kebede scores; Parker scores, Bhasera scores