Chippa, who were making all the running, were 1-0 up after 10 minutes when Benjani Mwaruwari beat the off-side trap, jinxed past keeper Nkosingiphile Gumede and kept his nerve to score in an empty goal.
But the Zimbabwean wasted a great chance just a few minutes later when a clumsy first touch allowed Gumede to make the save.
The KZN side’s defence was all over the place in the opening stages of the game, but Chippa failed to capitalise as Welcome Qalanto fired his effort wide of an empty net.
Abafana Bes’thende left their best chance for just before the interval, but after a great bit of play from Lucky Nguzana, Norman Smith’s first touch was poor and the chance was wasted.
The Chilli Boys had a perfect opportunity to extend their lead to two goals just after the restart, but Dlamini made a hash of his back-post shot after William Twala’s cross.
Chippa were made to pay for their wasted chances when the Durban side levelled the game on 54 minutes, defender Musa Bilankulu popping up in advanced position to head home Smith’s cross.
Just over 10 minutes later and Arrows took the lead, Smith smashing the ball into the roof of the net from five-yards out after Kassaly had failed to hold on to Nguzana’s shot.
The balance of the game saw the Chilli Boys doing most of the attacking, putting Gumede and his defence under some severe pressure.
But despite some close calls, which saw the ball bouncing around the Arrow six-yard box and even onto the bar, the visiting side were able to hold on for the crucial three points.