Gabadinho Mhango had a chance to grab an early lead in the third minute after he received a pass from Amr Gamal at the back post but he could not find the target.
The Urban Warriors were finding it hard to come out of their own half after 15 minutes as the Clever Boys pressurised them relentlessly in search of the opening goal.
Vincent Pule almost found the breakthrough in the 25th minute with a thunderous strike from 30 yards but it skimmed over the crossbar.
Stanley Menzo's troops started to show up after 35 minutes but their final ball always let them down.
Thabo Mosadi had a rare chance two minutes before halftime inside the box but his strike went wide.
The first stanza ended with both sides locked at 0-0.
Ten minutes into the second half, the visitors were set up with all the players behind the ball in an attempt to frustrate Gavin Hunt's charges.
Pule complained about a hamstring strain on the hour mark and was subsequently replaced by Daine Klate.
Klate nearly broke the deadlock in stunning fashion in the 70th minute but his acrobatic overheard kick inside the box sailed over the bar.
With 10 minutes to go, Gamal missed a sitter inside the box with the net gaping following good work on the right wing by Reeve Frosler.
The Clever Boys were unable to bypass the Ajax defence in the closing stages as they were forced to settle for a point on home soil.