The Cape side created numerous scoring chances on the day, but were let down by some poor finishing.
Ajax were on top for most of the first half, indeed for most of the match, keeping Stars pinned back in their own half.
Matome Madimabe pulled an early shot wide for the visiting team, but Ajax soon had chances as Diyo Sibisi shot just wide from a tight angle in the 14th minute, and then Thulani Serero was unable to beat Kennedy Mweene, seeing his shot bouncing off the Stars keeper before being cleared off the line.
Ajax were getting joy down their right flank, but again failed to round off a good move as George Maluleke fired over the bar after a square ball from Serero.
Franklyn Cale was far from his best and messed up a good chance when a heavy touch wasted a great opportunity after Sipho Nkosi had slipped at the back.
Stars looked a bit better after the break, but it was Ajax who had the first good chance of the half when Sifiso Vilakazi sent a glancing header wide in the 60th minute.
Kleinbooi Taaibos then sent a long-range just over the goal in the 65th minute before Vilakazi missed the chance of the game, failing to control Cale’s cross into the box when he found himself unmarked in front of goal.
Stars did have a couple of late chances as Aleni Lebyane beat Hans Vonk to a long ball in the 75th minute but saw his header go just wide, while ten minutes later Mpho Makola shot over the bar after an error from Derek Decamps.