The game was goalless but packed with incident.
Ajax, a four-time winner of the competition and a semifinalist last season, dominated possession and created a string of promising situations.
But the lively home attack, with 22-year-old Jordanian Musa Suleiman showing some eye-catching form, created the most dangerous chances.
Ajax conceded a string of free kicks in the second half and Noussair Mazraoui paid the price when a flailing tackle on Uros Matic earned him a second yellow card with 10 minutes to play.
Veteran striker Klass Jan Huntelaar, who came on with 12 minutes left, had a clear opportunity to win the game in added time, but the 36-year-old's tame chip was cleared.
"We gave the ball away too easily and we must improve next week," said Ajax attacker Dusan Tadic. "I expect the same compact defensive zone from APOEL in the second game. But we need to play much better."
While Ajax were disappointed with an away draw, Nicholas Ioannou, APOEL captain, was happy with his team's chances.
"We played really well," he said. "We defended very well and had some good chances at the other end to score. We were quite unlucky not to. We still believe we can go through."
Ajax take Dutch Super Cup with 2-0 win over PSV Eindhoven
There was only goal from open play in the night's three matches, but it was a pretty strike to give Slavia Prague a 1-0 victory in Cluj.
Nicolae Stanciu played a 28th-minute corner to Lukas Masopust, lurking outside the penalty area. The midfielder flighted the ball into the far corner of the net with the gentlest of long-range volleys.
"We practiced those corner kicks two days ago and I couldn't hit the ball well," said Masopust adding that team captain Tomas Soucek "told me today to try it with the side-foot and it worked."
Cluj coach Dan Petrescu was less impressed.
"Was it a pass or a shot?" he asked. "It was like table tennis."
Cluj won a penalty in the 79th minute, but Ondrej Kolar saved French striker Billel Omrani left-foot spot kick.
"I knew that the penalty-taking player always waits until the very last moment before kicking the ball, so I waited, did not lose my nerve and saved it," said Kolar. "It was my first saved penalty for Slavia."
In Austria, Linz ASK fell behind to Club Brugge in the eighth minute and despite a late siege of the visitors' goal, lost 1-0.
Centre back Gernot Trauner was caught in possession by Lois Openda and clumsily ran into the striker. Hans Vanaken slammed home the penalty kick.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ