The Ajax goal was scored by George Maluleka in the first-half.
The visitors played a pressing game from the start and it paid off in the eight minute when Vilakazi won possession in the Arrows half and initiated a quick counter-attack which saw Brent Carelse playing a perfect pass for George Maluleka, who buried a low shot into the back of the net.
The Urban Warriors could’ve doubled their league just three minutes later from a counter-attacking move when Khama Billiat played a low cross into the box, but Arrows goalkeeper Helton Da Rocha was able to grab the ball before Maluleka could get to it.
The Brazilian goalkeeper pulled off a one-handed save in the 25th minute to deny Granwald Scott’s curled effort following a poor clearance from Mzivukile Tom. However, it proved to be a costly save as he injured his shoulder and had to be substituted.
Young goalkeeper Nkosingiphile Gumede, who was making his debut, was called into action in the 46th minute to block a fierce left-footed shot from Maluleka who was looking for his second goal of the match.
The home side got their first shot on target in the second minute of added time when Philani Shange unleashed a first time shot from outside the box which was punched away by goalkeeper Sander Westerveld to keep Ajax ahead going into the break.
Gumede almost gifted Ajax their second goal of the match in the second half when he failed to control a harmless backpass but the young goalkeeper recovered to clear the ball off the line.
Gabuza thought he had equalised for Arrows five minutes later when he bundled in a cross from Philani Shange but the goal was chalked off as the striker had strayed slightly offside.
Substitute Katlego Mashego also came close in the 72nd minute when he made a great turn into the box and tried to nudge the ball past the advancing Westerveld, but the experienced goalkeeper was able to block the shot with his legs.
Three minutes later it was Gumede who made a brilliant save at the other end to deny a Khama Billiat header after a pinpoint cross from Tafadzwa Rusike.
Musa Bilankulu also saw his effort cleared off the line in the 85th minute, but the tall defender seemed to have handled the ball anyway.
Arrows will feel unlucky to get nothing from the game after the effort they put in during the second half, but Ajax Cape Town on the other hand could’ve sealed the match in the first half.