Ajax are top with 67 points and three matches remaining, six points ahead of Vitesse Arnhem who play their game in hand at Feyenoord on Sunday.
PSV Eindhoven, who are in third position and level on 60 points with fourth-placed Feyenoord, visit mid-table AZ Alkmaar on Saturday.
Danish teenager Viktor Fischer put Ajax ahead after 26 minutes when he headed in from close range following good work by Ricardo van Rhijn.
Seventh-placed Heerenveen delighted coach Van Basten, a former Ajax favourite, eight minutes into the second half when midfielder Sven Kums delivered a cross from the right and Alfred Finnbogason struck his 24th league goal of the season.
"We made it difficult for ourselves," said Ajax captain Siem de Jong. "We started okay but our performance levels dropped after we went in front."
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