The Celtic goals were scored by Moses Spandeel and Gert Shalkwyk while Mabhuti Khenyeza scored a late goal for Ajax.
Mark Mayambela looked lively for the home side early on and in the fourth minute he came close to creating the opening goal when his shot from a tight angle struck the base of the upright before being cleared off the line by the Ajax defender Brett Evans.
Ajax began to play their way back into the game and apart from earning at least five corners in the opening 20 minutes, Mabhuti Khenyeza and Sifiso Vilakazi both headed over the bar.
But it was Celtic who opened the scoring when a free flowing move involving Petrus Mahlatsi and Gert Shalkwyk ended in Moses Spandeel sweeping the ball home from 10-yards out in a central position.
The goal seemed to unsettle the Cape Town side, who had a couple of nervous moments in defence with Clayton Daniels in particular looking shaky, while in the middle of the park Nhlanhla Shabalala flirted with a sending off as his frustrations mounted.
The Urban Warriors had goalkeeper Andre Petim to thank for the fact that they went into the half time break with only a one goal deficit after he back-tracked to pull off a wonderful save after Shalkwyk had showed his brilliance, and confidence, with an attempted chip from nearly 50-yards out.
Two minutes after the restart Petim was at it again when he made a sensational save to prevent Spandeel scoring from a 25-yard free kick.
And there was soon more to come from the visiting goalkeeper – a minute later Schalkwyk burst clean through on goal, but Petim was on hand to make a brave block at the Celtic man’s feet.
But three minutes later Schalkwyk finally got the better of Petim when he beat the off-side trap before rounding the keeper and rolling the ball into the back of the net to make the score 2-0.
After Petim pushed away Mahlatsi’s angled shot in the 59th minute, Ajax started to enjoy more time on the ball, but a determined effort by the Celtic rear-guard ensured that the Cape side struggled to create any openings.
At the other end of the field Schalwyk continued to threaten, but directed a 66th minute effort straight at Petim and then a minute later chipped just over the bar.
Six minutes later Spandeel wasted another chance to add a third when he missed the target from close range.
Khenyeza struggled to make an impression throughout the game and his frustrating afternoon was illustrated by the picking up of a yellow card five minutes from time for an aerial foul on Celtic keeper Patrick Tignyemb.
Petim was again called into action with just two minutes on the clock when he made a diving save to push Spandeel’s shot to safety – and it would be fair to say that Craig Rosslee’s men could really have been on the receiving end of a hiding had their shot stopper not been in such good form.
The Cape side were somewhat fortunate to score a consolation goal with the final kick of the game after Khenyeza netted with a penalty following Mubiala’s foul.