Last season's UEFA Champions League semi-finalist named a strong starting XI that included several stars of its eye-catching 2018-2019 campaign, such as David Neres, Hakim Ziyech and Donny van de Beek.
But it produced a lacklustre and ill-disciplined performance, earning seven yellow cards and one red for Noussair Mazraoui.
The Dutch side looked the better of the two teams in the first half, but its display was lacking the decisive touch in front of goal.
After the break, APOEL began to offer more of a threat themselves and went agonisingly close in the 58th minute, when Giorgos Merkis' header hit the crossbar.
Andre Onana was then forced to make a stunning save 11 minutes later, getting down to palm away a Lucas Souza effort that was destined for the bottom-right corner.
Things got even more testing for Ajax towards the end when Mazraoui was shown a second yellow card for a needlessly clumsy tackle from behind, but they held on nonetheless.
Ajax hosts APOEL in Amsterdam for the second leg next Thursday (AEST).
In the day's other play-off clashes, Slavia Prague and Club Brugge claimed 1-0 away wins at Cluj and LASK, respectively.