The draw leaves the Urban Warriors placed ninth on the Absa Premiership standings with 31 points, while Dikwena stayed third on the league log with 44 points.
The first shot at goal went to the home side two minutes into the game and it was Erwin Isaacs who fired way over the target.
In the 14th minute, Bantu Mzwakali's good cross found his Ajax teammate Tashreeq Morris who guided the ball wide with his head.
The deadlock was broken four minutes later through Ajax striker Morris with a free header at the far post following good work down the right flank and a perfect cross from Nthuthuko Mabaso to make it 1-0 to his side.
The visitors then pressed Ajax for the equalising goal - Siyabonga Zulu's effort was blocked by Ajax defender Abbubaker Mobara in the 27th minute.
Ajax's towering centre-forward Nathan Paulse came very close to doubling his side's lead ten minutes before the break, but his header missed the target.
Dikwena had a promising start to the second-half as they threatened the Urban Warriors in the final-third and their pressure paid off in the 58th minute.
Former Orlando Pirates striker Mabena beat Finnish shot-stopper Anssi Jaakkola in the Ajax goal with a beautiful chipped finish to level matters on the night.
In the 69th minute, Stars shot-stopper Mlambo produced a fine save when he denied former Bidvest Wits winger Isaacs Ajax's second goal.
Ajax full-back Mosa Lebusa played a cross into the Stars box nine minutes later which found his teammate Toriq Losper who guided the ball inches wide of the target.
Nevertheless, Stars keeper Mlambo made late saves to ensure that the match ended in a 1-1 stalemate in Cape Town.