Miguel Timm scored the winner midway through the second half, after Henrico Botes had cancelled Sibusiso Vilakazi's opener.
The first half saw few scoring chances being created but it was the home side who showed more hunger and rightfully took the lead going into the break.
Sifiso Myeni had a chance in the seventh minute, but his shot sailed over the crossbar.
The deadlock was broken four minutes later when Sibusiso Vilakazi was put through by Sandile Sibande; the midfielder kept his composure to beat Siyabonga Mpontshane with a low shot across goals.
Myeni, who was giving Platinum Stars defenders all sorts of problems, continued to look for goal-scoring opportunities and in the 27th minute he saw his effort punched away by Mpontshane, while Ryan Chapman shot wide a minute before half-time.
Wits started the second half in high spirits and Myeni yet again tested the Stars goalkeeper, but Mpontshane was equal to the task and he pushed the ball wide of the upright.
The equalising goal arrived in the 51st minute when Henrico Botes finished from close range after receiving a pass from Nyauza Ntsikelelo.
However, it did not take long for Roger de Sa's men to restore their lead via a well-taken goal from Timm, who was given space to shoot inside the Stars penalty area.
The visitors were reduced to 10 men in the 68th minute when substitute Joseph Molangoane was given his marching orders for a foul on Myeni.
This proved to be the crucial factor, following the loss of another substitute, Reuben Thebakang, to injury.
There was to be no way back for Owen da Gama's side and Wits held on for their sixth win of the season.