Nkanyiso Mngwengwe's first-half goal was cancelled out by Prince Nxumalo's second-half header as the two sides took a share of the spoils.
Ajax went on the ascendency early on as Mark Mayambela found himself one-on-one with Nkosingiphile Gumede in as early as the first minute, but the Arrows keeper did just enough to force the effort wide of the target.
The visitors then had the ball in the back of the net through Mayambela, after Gumede excellently denied Nxumalo from 12 yards out, but the linesman incorrectly flagged for off-side.
It was Arrows who then found themselves in the lead when Mngwengwe rifled home from close range after Jody February made a mess of a corner-kick in the 13th minute.
The hosts almost doubled their lead in the 21st minute but for great defending from Roscoe Pietersen, who popped up to head off the line.
Gumede was again called into action to deny Mayambela as the midfielder drove a shot towards goal but the keeper palmed it clear just before the half-hour mark.
Nxumalo had a shy at goal just before the half-time break but his effort sailed wide of the target, with Ajax pinning the home side back into their own territory.
Two minutes after the restart of the second half, Pietersen should have done better as he flashed his shot inches wide of goal from an Ajax corner.
A subdued period saw both sides engage in a midfield battle for possession as neither keeper was tested.
Thabo Mosadi then had a chance shortly after the hour-mark as he drove towards goal from the right flank but flashed his effort wide of the far-post from an acute angle.
With 15 minutes left on the clock, Gumede made amends for a dismal clearance from an aerial ball into his area as he denied Mayambela for the umpteenth time in the match.
However, Ajax finally got their equaliser two minutes later as Nxumalo headed home at the back-post from a well-placed Mosadi corner-kick.
Ajax continued to probe for the winner as Grant Margeman forced Gumede into a good low save with a well-hit long-range shot with four minutes left on the clock.
In the end, Ajax would feel hard done by after having their first half opener incorrectly disallowed for off-side but will be happy to have salvaged a point.