Goals from Jan Vertonghen and Romelu Lukaku late on helped the Red Devils grab three more qualifying points in Athens, while Zeca was on target for the hosts.
It was Belgium's seventh victory in eight Group H matches, and the one which finally clinched passage to Russia 2018.
With just two games to go Martinez's men hold an unassailable eight-point lead over closest rivals Bosnia-Herzegovina, meaning they are guaranteed to finish in the group's top spot and take automatic qualification.
Belgium's success means that six out of the 32 World Cup spots are now occupied.
Hosts Russia, Brazil, Iran, Japan and Mexico are the other sides already assured of participation in 2018, while Germany could join them if the current holders beat Norway on Tuesday and Northern Ireland drop points to Czech Republic.
Russia 2018 will be Belgium's 13th World Cup finals, a number Martinez will hope proves to be lucky as the talented Red Devils gun for their first-ever title.