The Belgian international opened the scoring after 11 minutes after a brilliant pass from Christian Eriksen and headed his second seven minutes before the interval, moments after a straight red card for Samuel Scheimann.
Darren Maatsen pulled one back for Excelsior on the stroke of half-time but a converted penalty from Miralem Sulejmani and a goal from Nicolas Lodeiro sealed Ajax's first home win since August 26.
Groningen and NEC Nijmegen drew 3-3 on Saturday after Uruguayan David Texeira's hat-trick had given Groningen the lead three times.
Nijmegen substitute Melvin Platje scored two similar, well-taken goals in the final seven minutes - including an equaliser in injury-time - to salvage a point.
In other action Roda JC Kerkrade beat Graafschap Doetinchem 2-1 and ADO Den Haag brushed aside NAC Breda 3-0.
