Lucas Thwala had give Pirates a first half lead from the penalty spot after Teko Modise had been fouled.
There was an early opportunity for Benson Mhlongo, but he shot over the bar from just outside the box.
Pirates had the upper-hand during the early stages of the game, while the Clever Boys countered with intent.
After Thwala's penalty, Gert Schalkwyk got a great opportunity to extend the lead, but he failed to hit the target from close in front of goal.
Wits fought hard to get back into the game. The Students were especially strong from set-pieces, above all when Tefu Mashamaite moved forward.
However, it was again Schalkwyk who seemed set to score Pirates’ second goal, but his shot was directed straight at Wits keeper Francis Chansa.
Kadi then looked certain to score, but his powerful header from close range was brilliant saved by Josephs.
Wits got their goal in the 65th minute when Kadi scored from close range after an excellent cross by left winger Sifiso Myeni.
It was the first goal Josephs had conceded this season.
And he almost conceded a second late on when a long ball bounced awkwardly and headed for the top corner, but he recovered well to tip it to safety.