Ronald Koeman's side could not break the deadlock at De Goffert in the early Sunday kick-off and they could only increase their lead on second place PSV Eindhoven to six points while NEC are seven points above the drop zone.
In the afternoon matches on Sunday, third place Feyenoord defeated bottom club Volendam 2-0 at De Kuip.
Eby Smolarek gave the Rotterdam club the lead a minute before the break and Dirk Kuyt sealed the three points for the home side with a 76th minute penalty.
Csaba Feher's third-minute strike was enough to give NAC Breda a 1-0 win over struggling ADO Den Haag at the Fuji-Film Stadion.
Relegation-threatened Zwolle gave themselves hope of getting out of the bottom three after coming from two goals down to earn a 2-2 draw at Groningen.
The home side took a 2-0 lead into the break following goals from Sander van Gessel (18) and Paul Matthijs (44).
However, the visitors turned the match around with two second half goals in the space of a quarter of an hour from Albert van der Haar (70) and Mauro Almeida (85) to earn a vital point.
Zwolle stay three points adrift of Eredivisie safety with three matches remaining in the season.
Click below for match summaries:
De Eredivisie
FC Groningen 2-2 FC Zwolle
Feyenoord 2-0 FC Volendam
NAC Breda 1-0 ADO Den Haag
NEC Nijmegen 0-0 Ajax
Click here for an updated Eredivisie table.
