It took a clinical finish from substitute Tashreeq Morris to open the scoring before a superb free-kick from Granwald Scott made for a flattering scoreline and secured the three points.
With the win, Ajax rose to 37 points and sixth spot on the log as their top eight ambitions were strengthened.
In contrast, Tuks remain on 30 points for 10th place on the table as their objective of finishing the season in the lucrative top eight suffered a blow.
Just after the quarter hour mark, Denver Mukamba went close from a free kick from the edge of the area. His well-struck shot curved goalwards but was just inches over the crossbar as Ajax keeper Anssi Jaakkola was adjudged to have made a vital deflection.
In the 29th minute, Tuks had a good chance to open the scoring. Thabo Mosadi found space down the right, and whipped the ball in for Atusaye Nyondo waiting in the middle. Nyondo’s is first-time shot was fired into the posts to the relief of the keeper, who had put in a despairing dive to no avail.
Keagan Dolly wasted a great chance for the home side in the 39th minute. The Ajax midfielder made a menacing run starting near the halfway line, but once he glided into the Tuks box unhindered, deposited his left-footed attempt closer to the corner flag than goal.
In the 71st minute, Riyaad Norodien for the home side broke away from the Tuks defence. Receiving the ball near the halfway line the 19-year-old surged towards the box, but once inside opted to take a shot instead of passing to an unmarked teammate and his effort was sprayed into the crowd.
Ajax finally broke the deadlock in the 79th minute. Mosa Lebusa crossed into the area and Morris rose above the Tuks defence to bury the ball in the back of the net to make it 1-0 the the hosts approaching the final ten minutes of the encounter.
In the 90th minute, Scott doubled the scoreline in spectacular fashion. Awarded a free kick close to the left hand touch-line from 30 metres out, Scott produced a thunderous shot which clipped the crossbar on its way into goal.