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Frank de Boer's side threatened early on as Lasse Schone coasted down the left flank and fired a ball across the face of goal. The ball deflected into the path of Ricardo van Rhijn, but he failed to hit the target with a strike from the edge of the box.
Ajax had another good opportunity to take the lead when Ricardo Kishna found space down the left to whip a cross into the box for the advancing run of Arkadiuz Milik. The striker opted to go with a diving header rather than his foot, which proved to be the wrong decision as his effort was saved.
The home side took the lead just before the break when Milik was brought down in the penalty area by Marios Antoinaides. Schone took the spot kick and fired his effort past Urko Pardo with ease.
In the second half, Ajax upped the ante and they doubled their lead as they capitalised on a mistake in midfield which allowed Milik to raid upfield on the counter. The striker's shot was saved by Pardo, but Schone was on hand to put in the rebound.
The home side killed the game off in the 53rd minute when Kisha raided down the left and beat two defenders before lifting a cross into the box, and Davy Klaassen rose to power a header past Pardo into the top corner.
Ajax nearly added a fourth goal as a through-ball from Thulani Serero released the run of Kishna through the middle and one-on-one with Pardo. However, the keeper spread himself to narrow the angle, and made a good block with his body to deny the winger.
De Boer's men secured their place in the Europa League when they notched their fourth goal of the evening as Klaassen turned provider for Milik, who raced onto a through-ball and slotted his effort past Pardo.