A late goal from Bonginkosi Ntuli put the result beyond doubt, after Ntlantla Zothwane had opened the scoring late in the first half.
Ajax came close to taking the lead in the second minute but Khama Billiat could only curl his shot wide, after he was put through by Bradley Grobler.
The home side had an opportunity 11 minutes later when Musa Bilankulu collected a corner from Sibusiso Hadebe, but his effort lacked the pace to trouble Sean Roberts.
Then, in the 18th minute, Pavels Steinbors produced an acrobatic save at the other end to palm a powerful header from Grobler over the crossbar, before Billiat lifted his shot over the target five minutes later.
Grobler had yet another opportunity in the 32nd minute when he leaped up to meet a Billiat corner, but his header went wide of the upright.
Arrows took the lead 10 minutes before the break from a good team move which saw Zothwane timing his run to perfection to head Mzivukile Tom’s cross into the back of the net.
The Urban Warriors came close to leveling matters eight minutes into the second half when Toriq Losper showed good skill to shrug off his marker, but in the end his low strike was pushed wide by Steinbors.
Then substitute Koen van de Laak curled his shot wide of the post in the 62nd minute, before he was denied by the upright a minute later as Ajax continued to search for the equaliser.
The experienced Grobler will be disappointed with his effort on the hour mark, as he shot wide of the post after collecting a well-weighted through ball from Losper, who was a livewire for the visiting side.
The end-to-end action continued in the 72nd minute as Zothwane volleyed over the target from just inside the box, while Losper saw his headed effort palmed over the crossbar by Steinbors a minute later.
Ntuli poked a shot just wide before substitute Dillon Sheppard rattled the crossbar as the hosts looked to double their advantage.
The visitors had one last chance to net the equaliser in the 86th minute when Mosa Lebusa managed to sneak in at the far post, but he sent his volleyed effort over the crossbar.
However, Abafana Bes’thende finally managed to end the contest in the fourth minute of added time as Luyolo Mapolisa found Ntuli inside the box, and he turned and shot past Roberts.
The three points see Arrows up to 11th place with 16 points, while Ajax drop down to 12th with 15 points.