Twente, on 63 points with five matches remaining, beat PSV Eindhoven 2-0 on Saturday, when PSV slipped to second with 61.
Ajax endured a lacklustre start with an injury-hit defence as Gregory van der Wiel, Toby Alderweireld and goalkeeper Maarten Stekelenburg were all sidelined.
They livened up after 58 minutes when Spaniard Oleguer scored from close range after a blunder by Heracles goalkeeper Remko Pasveer.
Siem de Jong doubled the lead seven minutes later before Araz Ozbiliz added a third in the 81st.
ADO Den Haag beat Utrecht 3-2 to stay on course for a Europa League berth, remaining in fifth place with 51 points. Dmitri Bulykin converted a penalty for his 18th goal to go level with Nijmegen's Bjorn Vleminckx.
Sixth-placed Groningen beat VVV Venlo 3-2 and Vitesse Arnhem clinched a 2-1 derby win over NEC Nijmegen.
