Themba Ntumba scored the only goal.
The defeat for the Clever Boys extends their winless streak to seven games and they are sliding alarmingly down the standings after their usual promising start.
Dikwena, meanwhile, have broken into the top eight and are now eight games undefeated in the League.
Stars started brightly and scored the game’s only goal 12 minutes after the kick-off. Solomon Mathe set up Themba Ntumbi and the midfielder netted a superb long-range strike that ended up being the decisive moment of the game.
The rest of the first half saw plenty of perspiration from both teams as they looked to add to the scoreline, but neither Tapuwa Kapini nor Darren Keet were unduly troubled.
The second half was much of the same, though Keet was the busier of the two keepers as Platinum Stars looked determined to add to their advantage.
Wits threatened sporadically, but any hope they had of coming back into the contest were virtually eradicated with a quarter of an hour to play when they were reduced to 10 men.
Young defender Mzwanele Mahashe received his marching orders from the referee after picking up a second yellow card.
The hosts took their foot off the pedal and saw out the rest of the game in relative comfort to claim a deserved victory.