Amr Gamal had the first chance of the match in the sixth minute when he skipped past Erick Mathoho inside the box but his shot from a tight angle was saved by Itumeleng Khune.
Amakhosi countered a few minutes after with Bernard Parker combining with George Maluleka upfront, but Maluleka's shot from just outside the box went narrowly wide.
Mathoho should have opened the scoring in the 23rd minute but he got under the ball from Siphiwe Tshabalala's cross and headed over from six-yards out.
Steve Komphela's charges were reduced to 10 men as Wiseman Meyiwa was shown a straight red card in the 26th minute for a stamp on Daine Klate.
James Keene punished the visitors, who were still disorganised at the back, three minutes later by heading home from close range, 1-0.
The Clever Boys knocked the ball around with confidence going into the 40th minute but lacked the final pass to unlock the Amakhosi defence.
The Glamour Boys reacted to being a man down after the halftime break by bringing on striker Gustavo Paez at the expense of defender Daniel Cardoso.
The Clever Boys continued where they left off as they dominated the possession stakes after an hour and looked to attack the visitors down the flanks.
Paez missed a sitter in the 63rd minute after being sent through on goal by Willard Katsande, one-on-one with the goalkeeper he missed with the net gaping, however he was flagged offside nevertheless.
Klate was withdrawn in the 69th minute for Steven Pienaar for the hosts, while Dumisani Zuma replaced Parker for Komphela's troops.
Zuma missed a glorious opportunity to level the scores in the 74th minute but Darren Keet came out tops one-on-one with the Amakhosi forward.
Hendrick Ekstein came on four minutes later for the visitors in place of Philani Zulu as Komphela threw his last dice to try and turn things around.
Keene had a bandage wrapped around his head throughout the second half and in the last five minutes he could not continue as the bleeding could not be stopped by the medical team and was replaced by Elias Pelembe.
Keet was outstanding in the 90th minute as he leaped the highest to catch Tshabalala's cross into a crowded box and took the sting out of the Amakhosi attack.
Chiefs failed to bypass the Wits defence in the closing stages of the second half, as Wits held on for the win to progress to the final.