Forward Sulejmani put Ajax ahead eight minutes into the second half, netting from close range, and doubled the lead 12 minutes from time. They added a third when 18-year-old Davy Klaassen scored in his first league appearance.
Feyenoord had gone behind to Waalwijk after a Ricky ten Voorde goal in the first half but their hosts then had Robert Braber sent off after 62 minutes.
John Guidetti equalised when he curled the ball around keeper Jeroen Zoet before a deflected shot from Jerson Cabral earned Ronald Koeman's men the three points.
In other action, Twente Enschede lost more ground on leaders AZ Alkmaar after being held 0-0 at home to Vitesse Arnhem, while Excelsior Rotterdam drew 1-1 with ADO Den Haag to leave VVV Venlo propping up the table.
AZ Alkmaar, 2-0 winners against Utrecht on Friday, are top with 34 points from 13 matches, three points ahead of PSV Eindhoven with a game in hand. PSV thrashed Groningen 6-1 on Saturday.
Twente are third on 27, three points above fourth-placed Ajax and fifth-placed Feyenoord.
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