George Maluleke and Stanton Lewis scored for Ajax, while Mzuvukile Tom scored for Arrows.
It was an entertaining game in which both teams played their part in an open and fast-paced contest –Ajax enjoying more of the play, but Arrows always a threat with their pace on attack.
Ajax were on top from the kick-off, and Maluleke made no mistake in the 11th minute when he slotted home at the near post from Sameehg Doutie’s cross, which had followed an intricate build up.
Arrows barely got into the Ajax half of the field, yet they managed to fashion and equaliser in the 25th minute when Tom squeezed home a shot from a tight angle.
The visiting team ended the half strongly as both Vusumuzi Vilakazi and Nhlanhla Zothwane got shots in from range.
Abafana Bes’thende also started the second half strongly, but Ajax went back in front after 51 minutes when Lewis converted superbly after a through ball from Granwald Scott.
Thamsanqa Gabuza and Koffi Tanoh both came close to making it 2-2, the former heading straight at Hans Vonk from seven yards out, the latter striking the bar in the 78th minute.
Ajax also had late chances as Diyo Sibisi’s shot from the edge of the area flew marginally wide and then Scott had a goal ruled off-side.
Arrows were not able to create any real opportunities in the final 10 minutes of the game as Ajax defended resolutely to advance into the last four.