Although the visitors dominated possession, they were unable to make it count as the hosts came away with maximum points courtesy of a first-half strike from Matthew Pattison.
Arrows created the first threat in the 11th minute when Dillon Sheppard delivered a free-kick into the box, but Joseph Musonda was unable to hit the target with his header.
That proved to be a costly miss as Wits took the lead four minutes later through Pattison, who collected a pass from Calvin Kadi before calmly slotting over the goalkeeper.
The visitors then came close to levelling matters in the 23rd minute when Aaron Mokoena lost possession, but Nkosinathi Ogle’s shot went wide of the target.
Seven minutes later Kadi came close to extending the lead when he latched onto a flick from Thembinkosi Fanteni, but he shot straight at the goalkeeper before firing another attempt over the crossbar moments later.
After the break it was Arrows yet again who came close to finding the back of the net in the 57th minute when Thanduyise Khuboni played a brilliant long pass to find Jabulani Nene, but his header was kept out by a great save from Steven Hoffman.
The Clever Boys then found themselves with one man less in the 65th minute when Ebrahim Seedat received his second yellow card in, but they made up for their numerical advantage by remaining disciplined at the back.
Antonio Habas Lopez’ men came close to scoring another goal against the run of play six minutes later when Arrows defender Musa Bilankulu almost found the back of his own goal, but his clearance went over the bar.
Muhsin Ertugral tried to sharpen his attack as he brought on Norman Smith in place of Latvian defender Kjauklis, and the move almost paid off right at the death when the substitute shot on target from close range, only to be denied by a spectacular save from Hoffman.