The opening exchanges were tactical, with neither side wanting to give anything away too cheaply early on.
The visitors grew into the game and were bossing the Chilli Boys, making their advantage tell in the 21st minute through Vincent Pule after a period of sustained pressure.
Lehlohonolo Majoro had a chance to double The Clever Boys lead in the 37th minute but his strike failed to find the target.
Daniel Akpeyi was forced to produce a decent stop just before the break when Sifiso Myeni whipped in a cross that found Majoro, his header tipped over the bar by the Chippa shot-stopper.
Linda Mntambo looked to get Teboho Moloi’s side back into the game 12 minutes into the second half, Darren Keet equal to his curling left-footed effort from just inside the area.
Bergman managed to draw The Chilli Boys level with 10 minutes left on the clock.
Myeni almost bagged the three points for Hunt’s men when he struck the woodwork with an attempt from outside the box.
The draw sees Bidvest Wits stay in 15th spot with Chippa United in 8th spot on the Absa Premiership log.