By Peter ORourke
Last Updated: 01/01/70 1:00am
Ronald Koeman's men had the chance to go nine points clear at the top, but that never looked likely once Mika Vayrynen fired Heerenveen in front a minute before the break.
The hosts doubled their lead just before the hour mark with Richard Knopper netting.
Vayrynen made the game safe for Heerenveen with the third goal and his second of the game on 70 minutes.
Jesper Hakansson piled on the misery with the fourth on 82 minutes before Peter Hansson put through his own net four minutes from time to give Ajax a consolation.
ADO Den Haag boosted their survival hopes with a surprise 1-0 win over Roda JC.
Former Ajax ace Cederic van der Gun grabbed the all-important winning goal for the hosts on 19 minutes.
NAC Breda were held to a 1-1 draw by FC Groningen at the FujiFilm-Stadion.
Csaba Feher fired NAC in front on 33 minutes, but Chris de Witte's goal on the stroke of half time earned Groningen a point.
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