Newly promoted Zwolle have been the Dutch top-flight's surprise package in the early weeks of the new campaign, dropping just two points in five games prior to their trip to the Amsterdam Arena.
However, Frank de Boer's side put an end to their unbeaten start by maintaining their perfect home record thanks to Thulani Serero's second-half strike and an own goal from Maikel van der Werff.
The teams went in level at the break after a tight first half, but South Africa international Serero broke the deadlock with 18 minutes left to play, before Van Der Werff put through his own net four minutes later.
Giovanni Gravenbeek pulled one back for Ron Jans' men in the 89th minute, but Ajax held on to move up to third in the table.
Despite their defeat, Zwolle remain top of the pile after the Eredivisie's only other unbeaten team, PSV Eindhoven, failed to take advantage by being held to a 2-2 draw at Twente.
Shadrach Eghan gave Twente the lead in the 17th minute, before Georgino Wijnaldum drew Phillip Cocu's side level shortly after the hour mark.
Quincy Promes then restored the hosts' advantage, but Memphis Depay earned PSV a point seven minutes from time.
Elsewhere, Cambuur followed up their impressive draw at PSV last time out with a 2-0 home win over Heracles thanks to Michiel Hemmen's first-half strike and a Jason Davidson own goal on 88 minutes.
Saturday's other fixture, Ado Den Haag's home game against Vitesse, was postponed due to a waterlogged pitch.
