The Brazilian made no mistake from 12 yards to secure a share of the spoils, but the Cypriot side had to withstand intense pressure in the closing minutes.
After controlling the early exchanges Frank de Boer's side opened the scoring two minutes before the half-hour mark as Lucas Andersen netted his first European goal.
Both sides wasted second-half chances to take the lead, with Lasse Schone and Cillian Sheridan guilty of poor finishing.
The draw means Ajax have picked up a point from each of their matches in Group F so far, keeping them ahead of APOEL, who were beaten by Barcelona on matchday one.
Seven minutes later Ajax produced an almost carbon copy of the earlier move but once again the Iceland international was unable to convert as Klaassen's cross eluded him.
The Dane played a neat pass into Schone, who returned to the starting line-up following a groin injury. Schone's effort was saved by Urko Pardo but Andersen pounced on the rebound.
A spot-kick was awarded despite Ajax protests and Manduca, in for Tomas De Vincenti, cooly slotted home from 12 yards.
As half-time approached APOEL, having soaked up more Ajax pressure, should have taken the lead but Sheridan was agonisingly short of converting Manduca's cross.
Nine minutes after the break both sides had a chance to take the lead in the space of 30 seconds, but Schone's effort was weak and Sheridan could not divert a header on target at the other end.
APOEL felt they should have had a man advantage on 56 minutes when Cillessen brought down Sheridan outside the area. However, the Netherlands goalkeeper was only booked and Mario Sergio wasted the resulting free-kick.
Cillessen then came to Ajax's rescue as he got down brilliantly to keep out a low, 20-yard drive from Mario Sergio.
He very nearly turned provider too as his long ball forward was picked up by Sigthorsson, whose effort was blocked by Pardo.
Sigthorsson's frustrating night in front of goal continued as he saw a looping header land on the top of the goal from Niklas Moisander's free kick.
One of APOEL's rare attacks in the second half nearly resulted in a home victory but substitute De Vicenti was flagged offside, meaning his neat chipped finish did not count.
