The contest failed to live up to its billing as one of the greatest fixtures in Dutch football, with neither side serving up their best football.
Feyenoord arguably produced the better openings with Colin Kazim-Richards shooting narrowly wide and Jean-Paul Boetius having an effort cleared off the line as Frank de Boer's Ajax struggled for ideas in front of their home fans.
Jop van der Linden's 43rd-minute penalty proved decisive as Go Ahead Eagles snapped their five-match winless run in a 1-0 defeat of ADO Den Haag.
Strugglers NAC Breda were held 0-0 at home to Willem II, while Groningen twice let the lead slip in their 2-2 draw with Utrecht at Euroborg.
A familiar story unfolded after the break when Michael de Leeuw made it 2-1 in the 51st minute, only for Utrecth to restore parity once again through Yassin Ayoung five minutes later.
