Frank de Boer's men needed only a draw from their final Champions League Group F fixture to finish third in the pool, but wrapped up a spot in European football's secondary club competition in style.
Lasse Schone scored either side of half-time before Davy Klaassen and Arkadiusz Milik added a goal apiece as the Dutch champions ran riot against their Cypriot counterparts.
Having created the better of the first-half chances, Ajax were made to wait until the stroke of half-time to move in front.
Marios Antoniades upended Milik in the area with Schone applying a confident finish from the spot, despite Urko Pardo going the right way.
Schone picked up where he left off after the break and double his side's advantage with a cool finish after a quick counter five minutes into the second period.
APOEL's task was made almost impossible when lively 19-year-old winger Ricardo Kishna jinked through the visiting defence and crossed for Klaassen to head in a third soon after.
And there was time for the ever-dangerous Milik to get in on the act, as the group's bottom club APOEL were outclassed.
After persistent play down the right from Schone, Ricardo van Rhijn curled an effort over the crossbar five minutes in for Ajax as APOEL initially struggled to grow into the game.
Nektarios Alexandrou had a shot blocked by Nick Viergever on the visitors’ first foray forward before Schone took a touch too many in the area and was crowded out after purposeful play down the left from Kishna.
While Ajax were without injured striker Kolbeinn Sigthorsson, Milik almost opened the scoring shortly before the half-hour mark but saw his stooping header kept out by Pardo.
Milik - on loan from Bayer Leverkusen - then had a free-kick deflected off target before Schone gave the Eredivisie champions a deserved lead before the break.
After Milik was clumsily brought down by Antoniades, Schone found the bottom left corner.
While APOEL started the second half positively, they carelessly gave away possession in midfield with the ball falling nicely for Schone.
The Denmark international played in Milik, but after the Pole was initially thwarted, he laid the ball back on for Schone who made no mistake to effectively tie up the match.
Just three minutes later, Kishna cut in from the left and evaded the attentions of a number of APOEL defenders to loft a cross in for Klaassen - who powered a downward header past Pardo.
Klaassen then turned provider for Milik 16 minutes from time to ensure Ajax take something from a difficult group that saw Barcelona and Paris Saint-Germain progress to the knockout stages.
