Needing just a win to qualify for next summer’s tournament in Russia, Belgium initially struggled at the Karaiskakis Stadium as the hosts threatened on numerous occasions.
Chelsea goalkeeper Thibaut Courtois made a superb one-handed save to push a first-half effort onto the post, but Vertonghen struck after the break to delight the travelling fans.
With the scores still level with 20 minutes remaining, the Tottenham defender took a touch to set a pass from Spurs team-mate Mousa Dembele before swerving a fine 25-yard effort into the bottom right-hand corner of the net.
Belgium’s joy was short-lived as Courtois was finally beaten two minutes later, with Zeca smartly volleying home an inviting cross from Georgios Tzavellas.
That put Belgium’s hopes of automatic qualification in doubt, but the Red Devils restored their lead 60 seconds later.
Chelsea forward Eden Hazard came off the bench to win a free-kick, and Manchester United forward Lukaku glanced a header home from Thomas Meunier’s curling cross.
Hazard was bright in the final stages as he went close as he ran at Greece’s tiring defence, though Belgium were unable to add to their one-goal advantage.
The victory in Piraeus means Martinez’s men have now qualified from Group H, with Martinez hoping to lead his talented squad to glory in Russia next summer.