While all the goals came in an action-packed first half, Ajax deserved their win as they were the dominant side throughout the 90 minutes.
The early stages of the game were scrappy as both sides tried to get a hold of the ball in the middle of the park.
It was Ajax though who enjoyed a territorial advantage and pressed forward in search of the opening goal.
Russell Mwafulirwa enjoyed the first chance of the game when he shot over the bar from outside the box, while in the 12th minute Celtic's Lebohang Mothibantwa was unable to get enough on his header to beat Hans Vonk.
Two minutes later Ajax debutant Dipsy Selowane made no mistake as he got the opening goal, steering the ball into the net from close-range after Nathan Paulse flicked on a throw-in.
Following the goal, the Urban Warriors wasted two glorious chances to increase their lead as first Mwafulirwa succeeded only with a fresh-air shot right in front of goal and then Mfundo Shumana hesitated too long and had two attempts in succession cleared off the line.
Phunya Sele Sele staged a brief comeback and in the 32nd minute when Lebohang Mothibantwa crashed a rocket of a shot past Vonk from the edge of the area after being teed up by Moses Spandeel.
The goal however spurred Ajax back into action and two minutes later the homeside were back in front when a Brett Evans free kick found its way through the Celtic defence, leaving Erduardo Ferreira with a simple tap-in.
There was more to come for the Cape side 10 minutes later when a great through ball by Enoh Eyong released Mkhanyiseli Siwahala on the right flank.
The Ajax youngster showed great composure to make sure his first touch took him in on goal before beating Posnet Omony with a clinical shot into the corner of the net.
With the restart of the second half, Phunya Sele Sele coach Khabo Zondo must have been a relieved man to see Gary Goldstone's attempted clearance go just wide of Omony's upright.
After that the game deteriorated slightly – a battle for supremacy in the centre of the park resulted in some scrappy play and a couple of yellow cards.
In the 70th minute Ferreira should have scored a fourth, but he failed to connect with the goal at his mercy.
There was no doubt that Ajax were remaining in the ascendancy in the second stanza and the impressive Eyong nearly grabbed a fourth when his 25-yard shot fizzed just wide of goal.
Sifiso Vilakazi was given a chance to emulate Selowane's goal on debut when he was put through on goal in the 79th minute, but the former Free State Stars man had his shot blocked by Omony.
Celtic rarely threatened in attack in the second stanza and the closest they came to scoring was via the head of Ferreira, who came within a whisker of putting the ball into his own net.
While the Urban Warriors were not able to add a fourth despite their attacking endeavors, coach Craig Rosslee would have been more that happy with the score-line which enabled his side to maintain their top position on the PSL log.