The Urban Warriors had their fair share of chances in an entertaining game, but had to wait until 20 minutes from time before they could cancel out Stars' early goal.
The visitors were put onto the back foot as early as the fourth minute when Jimmy Kauleza blasted Stars ahead with a shot from the lefthand side of the penalty area.
Ajax tried in vain to level matters as Granwald Scott made inroads into the Stars defence, but his crosses to Nhlanhla Shabalala in the sixth minute and to Nathan Paulse in the ninth minute were both saved by goalkeeper Kennedy Mweene.
Some determined defending by Ea Lla Koto then saw Collins Chabalala block Eyong Ehoh's shot in the 14th minute, before Eduardo Ferreira went wide with a header for the Cape side four minutes later.
After weathering the storm from Ajax, Stars went in search of an insurance goal which saw Motseothata November's shot being blocked by Ferreira, while Prince Olomu's 20-yard effort was saved by keeper Hans Vonk.
Moses Mbuyane had another good chance for the hosts in the 32nd minute but shot wide after being supplied by Kauleza, while for Ajax, Shabalala headed wide of goal from Bageta Dikulu's 38th minute free-kick.
Further chances fell to Stars when Mbuyiselo Sambu failed to hit the target from close-range, and then Kauleza had his free-kick tipped round the upright by Vonk in the 43rd minute.
Ajax enjoyed the first two chances after the restart when Mfundo Shumana had his shot blocked by Sipho Nkosi and then Dikulu sent his free-kick sailing over the bar in the 52nd minute.
Stars replied with a few opportunities of their own, but Olomu failed to induce a save from Vonk with his shot, while Mbuyane headed over the bar in the 59th minute and missed the target in the 67th minute.
The Urban Warriors finally got the equaliser they desperately sought when Shumana slotted home a 12-yard angled shot with his left foot in the 69th minute.
Following the equaliser, both sides had their moments in attack, however the only chance to snatch a winner fell to Stars' Matoma Madimabe three minutes before time, but he sent his shot from the edge of the area wide of the target.
The result leaves the Cape Town side on 44 points, three adrift of league pace-setters Supersport United, with both sides having played 25 matches. Santos have 42 points from 35 games.