Van Dijk converted from the spot after Denzel Dumfries was fouled in the box to edge his team up to second place in Group B.
Greece coach Gus Poyet received a red card for his protestations.
The Netherlands are level on points with third-placed Greece but lead the head-to-head having beaten them twice.
If the Dutch now beat the Republic of Ireland and Gibraltar in their final two games they will be guaranteed to reach next summer’s tournament in Germany behind France, who have already qualified from the group.
Greece have just one game left to play – at home to France.
