Wits threatened in the early stages of the half with Amr Gamal heading wide of the upright after eight minutes.
Gavin Hunt's charges continued to dominate in the first half, but they were let down by their decision-making in the final third.
The Chilli Boys, meanwhile, struggled to carve out chances in the half as they spent most of the game trying get the ball off the home side.
Wits fashioned a couple half-chances in the final 10 minutes of the half, but they failed to trouble Chippa goalkeeper Daniel Akpeyi as the sides went into the break goalless.
The hosts continued from where they left off in the first half as Gamal headed wide of the upright after 52 minutes.
Five minutes later, Teboho Moloi opted for a change as Andile Mbenyane replaced Mpho Mvelase, before Steven Pienaar replaced Xola Mlambo a few minutes later for the visitors.
Chippa eventually broke the deadlock in the 76th minute as Samuel Julies slotted a low left-footed effort into the bottom corner, after some good work by Paseka Mako, 0-1.
Hunt threw on James Keene for the final 10 minutes as they pushed for an equaliser.
However, the Chilli Boys managed to seal the win in the 85th minute with a superb curling effort by Julies from 20-yards out, 0-2.