Their win sees Wits leapfrog into second place in the standings while the team from PE currently languishes in sixth position.
The two sides had gone into the second round with one point each, after both had notched up goalless draws in their opening fixtures.
However, Madibaz head coach Graeme Harrison remained positive, saying the result was not an accurate reflection of his squad's performance.
"It was a very close game and I wouldn't say that Wits necessarily dominated us," said Harrison.
"I think we just had a lapse of concentration for a while, which allowed them to sneak in a goal."
Wits substitute Graeme Dor managed to open the scoring midway through the second half to secure the win for the Johannesburg team.
"It was just one of those games where we couldn't find our rhythm. We couldn't get past their defence and the ball just didn't roll for us," said Harrison.
The visitors' confidence was also dealt a blow when star striker Kieran Koert was sidelined within the first five minutes with a shoulder injury.
"That said, we can't just rely on Koert and Cloudius Sagandira to score all the goals," said Harrison.
"We need all our players to come to the party and create those opportunities as well."
He said although things had not come together as planned on Monday night, his players were ready to come back fighting next week.
"The boys know what is at stake. They are disappointed and know that they need to deliver next time around."
Harrison added that it was still early days and that the Madibaz had a number of chances to move up on the log.
"We are not panicking yet. We know that we need to create more goal-scoring opportunities and convert those chances into goals if we want to win games."
He said the team would focus on their attacking play ahead of next week's game.
The Madibaz will take on the University of Pretoria at the Tuks Sport Stadium in Pretoria. The match kicks off at 5pm.