The visitors had a chance to score from a free-kick just nine minutes into the game, but Kudakwashe Mahachi’s effort sailed just over.
In the 16th minute, Arrows forward Helings Mhango came very close to netting when he challenged Chippa goalkeeper Daniel Akpeyi, but the ball missed the target.
The in-form Malawi international then found some space just outside the Chippa box in the 33rd minute and unleashed a powerful shot which failed to trouble Akpeyi.
Ten minutes after the restart Buyani Sali forced Mbaeva into a decent save as the home side searched for the opening goal.
Andile Mbenyane shot over in the 68th minute, before Thamsanqa Sangweni’s dangerous curling attempt from a corner-kick was easily gathered by Mbaeva.
Xoli Mlambo came closest to breaking the deadlock with 10 minutes remaining, firing a bullet shot from outside the area, only for Mbaeva to produce a stunning save.
The draw leaves the Chilli Boys placed seventh on the Absa Premiership log, while Abafana Bes’thende remain ninth.