Celtic were keen to end a run of six matches without victory, with Deon Hotto bursting down the left flank to draw a save from Brandon Petersen in the opening five minutes.
Ajax came out strong too and had Zambian Rodrick Kabwe asking questions off Patrick Tignyemb, who responded by coming quick off his line to avert Yannick Zakri from profiting minutes later.
Another cross was floated in by Kabwe, who on this occasion managed to find Zakri, but the striker failed to direct his header on goal.
Celtic looked for a half-time lead after Jacky Motshegwa combined with Ndumiso Mabena inside the box, only find the side-netting minutes from the break.
Siwelele finally went ahead five minutes after the break when Ronald Pfumbidzai broke down the left to beat Petersen with a cross-cum-shot.
This led Muhsin Ertugral to make his second substitution as Grant Margeman replaced Toriq Losper a few minutes later.
They made their final change in the 63rd minute with Tendai Ndoro replacing Zakri, while Tignyemb denied Margeman from point-blank range later on.
Mario Booysen came up with their final chance at finding the equaliser after picking up a Tercious Malepe cross, but the former was unable to find the target as Siwelele walked away victorious.