The visitors had taken the lead through Eddie Ngalo, but a Nathan Paulse penalty and Sibusiso Gumede own-goal ensured a great fightback from the Urban Warriors.
Aces made all the early running, getting in a series of early shots at the Ajax goal.
Thanduyise Khuboni pulled his second-minute shot from inside the box wide after he had been teed up by Dino Ndlovu, Collins Mbesuma failed to trouble Anssi Jaakkola with an attempted chip, and Aubrey Ngoma and Miguel Timm both shot wide of goal.
The Urban Warriors had to wait until the 15th minute for their first chance – Toriq Losper’s first-time shot from outside the area going wide, before Erwin Isaacs’ header was blocked by the Aces defence two minutes later.
But it was the Mpumalanga outfit who were to draw first blood –Ngalo nodding in on 23 minutes from close range after Jaakolla had pushed Mbesuma’s initial header into his path.
The Urban Warriors came close to mustering a reply eight minutes before half-time, but Tashreeq Morris’ well-struck volley went straight at visiting keeper Jackson Mabokgwane.
Both sides had chances after the break, but Timm fired a low drive straight at Jaakkola after which Franklin Cale saw his spectacular scissors-kick at the back post going narrowly wide.
Ajax began to enjoy more and more ball possession, and were handed a lifeline on 69 minutes when they were awarded a penalty after Ngalo was judged to have fouled Mzwakali. Paulse made no mistake from the spot.
Ten minutes later and Ajax were in front when Gumede could only succeed in putting Mzwakali’s cross into his own net.
The Urban Warriors were on top for most of the remainder of the game and Aces unable to mount any kind of come-back as they remain winless in the league in 2015.