Frank de Boer's champions have endured an unconvincing start to the campaign, winning two, drawing twice and losing once in their opening five games.
Zwolle, by contrast, won their first four games and top the table, with their 1-1 draw with Utrecht prior to the international break marking the first time this term that Ron Jans' men have dropped points.
However, Ajax will be confident of inflicting Zwolle's first league defeat of 2013-14, having done the double over them last season, scoring seven goals in the process.
Second mets third when PSV Eindhoven travel to Twente. PSV know that they will go top with a win coupled with a Zwolle defeat, and the onus is likely to be on Belgian attacker Zakaria Bakkali to add to his tally of three league goals so far this campaign.
PSV have yet to taste defeat in 2013-14, but they face a stern test at De Grolsch Veste, where they have not won in the league since 2005.
Feyenoord made it back-to-back Eredivisie wins following a poor start to the season with a 4-0 win over Roda JC in their last encounter, and will look to build momentum against NEC Nijmegen, who sit bottom of the league with just two points.
AZ take on Go Ahead Eagles at the AFAS Stadion and, although they possess a dynamic attacker in American Aron Johannsson, they will have to be wary of the duo of Erik Falkenburg and Marnix Kolder, who have seven league goals between them for Foeke Booy's side.
Marco van Basten's Heerenveen host Groningen with the league's top scorer Alfred Finnbogason hoping to add to the six goals he has netted so far, while Vitesse will be out to make it four games without defeat against ADO Den Haag.
Elsewhere, Utrecht host RKC Waalwijk, Cambuur meet Heracles and Roda take on NAC Breda.
