Brent Carelse, Brett Evans, Matthew Booth and Lebogang Manyama got the goals for Ajax, while Rodney Ramagalela and a Kingston Nkatha brace made it three for Leopards.
Ajax dominated the opening stages, playing some neat and free-flowing football.
Their dominance was also transferred into superiority on the score-sheet when, after just two minutes, a poor clearance from a Leopards player meant the ball fell to Carelse, who scored with a well-placed volley.
Ajax then had Sander Westerveld to thank for keeping their lead intact when he made a fantastic reflex save from Thomas Madimba.
But there was no denying Lidoda Duvha their equalising goal in the 16th minute when Ramagalela scored with a well-taken low drive from 18-yards out.
The game remained open and fast-paced, with both teams intent on attacking.
The visiting side were to score next, taking the lead after 35 minutes as Nkatha rose well in the box to glance home a corner-kick.
Ajax, however, were soon back on level terms as Evans slammed home a shot from 30 yards out, which Posnett Omony should have kept out.
In first half injury time the Cape side were back in front again as towering centre-back Matthew Booth powered home a header.
Ajax controlled the game more in the second half, but had to wait until the 76th minute for their first real chance, which saw Manyama's volley tipped over by Omony following Khama Billiat's cross.
George Maluleka nearly got on the score-sheet a few minutes later, but his curling effort landed on top of the net.
Ajax seemed to be cruising, but there was some late drama as Nkatha got his second of the game with a header from Kethokwakhe Masuku's free-kick.
But Ajax struck back even deeper into injury time, with Manyama hammering the ball into the roof of the net to secure a late win.