Ryan Moon came off the bench to hand Chiefs the lead before fellow substitute Knox Mutizwa grabbed a dramatic equaliser late on.
The hosts had a great chance to get the opener in as early as the third minute as Pule Ekstein sent a threatening ball into the box, which fell for George Maluleka, whose shot was cleared in the nick of time by Romario Dlamini.
Arrows had an opportunity to break the deadlock after the half-hour mark, when Daniel Cardoso was dispossessed in an advanced position and Siphelele Magubane was sent away on a counter-attack – five versus two – but the winger selfishly opted to go for glory, with his shot taking a deflection and allowing Itumeleng Khune to make a comfortable save.
There was little to separate the two sides in the first-half, with chances coming few and far between.
The second half was a scrappy affair as Chiefs dominated possession but struggled to trouble Nkosingiphile Gumede in the Arrows goal.
With the Arrows defence holding steady, the home side were forced to try and find an opening from range, with Ekstein, Gustavo Paez and Willard Katsande sending efforts wide of the mark.
Substitute Moon then finally opened the scoring, bagging his first ever Chiefs goal in his third appearance, as he cooly slotted home from close range in the 77th minute.
However, Mutizwa came off the bench and proved a hero for the visitors as he bagged an equaliser in the final minute of stoppage time, capitalising on a lapse of concentration at the back to head home from a cross.