Arrows wasted no time surging ahead when Nkanyiso Mngwengwe headed home a corner on the near side on seven minutes.
Before that, the hosts missed the chance to go ahead from the spot after a foul on Siboniso Conco though Limbikani Mzava saw his effort saved.
The momentum on their side, Arrows closed in for a second but Knox Mutizwa’s hurried effort raced far away from goal.
Lerato Lamola found a long ball up field on the near side and contemplated a shot from range, but blasted over the top instead.
Polokwane got their first shot on goal albeit after 23 minutes when Salulani Phiri shot horrifyingly wide of target.
Arrows were holding firm to their lead despite the few threats City posed with Rendani Ndou amongst others.
The Rise and Shine kept pushing and were asking more questions, with the desired effect in front of goal missing.
The ball finally rolled in their favour as Arrows finally bowed to the pressure, with Rodney Ramagalela lashing home the equaliser from the far side on 41 minutes.
On 51 minutes, Mutizwa took a free-kick from the right side and it found its way on target but Chigova dived to make the save.
Within minutes, Lamola ran down the wing and played in a cross for Mutizwa to have a crack at goal but Chigova made another goal-wrenching save.
Ramagalela was put into space on the near side, and opted for a shot at goal but it sailed across the face of goal on 60 minutes.
In the latter stages, substitute Wayde Jooste got fed a nice ball from the far side but shot straight at Chigova who saved easily.