Schone opened the scoring from the penalty spot on the stroke of half-time before doubling his side’s advantage at the Amsterdam ArenA shortly after the beak.
Davy Klaassen headed in the third with Arkadiusz Milik’s low strike in the 74th minute wrapping up a comfortable victory to make sure of third place in the standings.
Reigning Eredivisie champions Ajax knew they could not reach the knockout stages of the Champions League but that any positive result at home to APOEL would secure Europa League football.
However, early in the game it was APOEL, who could also progress with a win in Amsterdam, who took charge.
Nuno Morais sent a shot over the bar from just outside of the area for APOEL in the second minute to fire an early warning shot to the Dutch hosts, who replied with Ricardo Van Rhijn’s curling strike which went a similar way shortly after.
Ajax defender Niklas Moisander then blocked a close range shot by Georgios Efrem before Lucas Andersen cleared a corner as the home side became under a bit of pressure.
Arkadiusz Milik saw a good effort denied at the other end in the 25th minute when APOEL goalkeeper Rafael Urko blocked his header from a central position in the area.
However, Ajax claimed the lead shortly before the break from the penalty spot when Marios Antoniades hacked down Arkadiusz Milik in the area in the 44th minute.
Schone stepped up to take the spot kick and placed it to the left of Urko to put Ajax one step closer to securing their place in the Europa League.
The Ajax midfielder then doubled his side’s lead five minutes into the second half with a low strike from the middle of the area.
Klaassen’s headed goal in the 52nd minute sealed Ajax’s progression to the second tier of European competition.
The midfielder got onto the end of Ricardo Kishna’s cross from the left to head past Urko from close range.
Milik added the gloss with a strike from the middle of the area from Klaassen’s cross to wrap up an emphatic win for Ajax in front of their home crowd.