Holding a 3-1 advantage from the opening leg, Fernando Santos' men arrived in Bucharest looking to wrap up the tie and they all but achieved that with a first-half strike from Konstantinos Mitroglou.
A bizarre own goal from Vasileios Torosidis early in the second half pulled Romania level on the night, but there was to be no dramatic comeback as Greece booked their ticket to Brazil 4-2 on aggregate.
It took a quarter of an hour for the match to come to life at Bucharest's National Arena and it was Giannis Maniatis who fired things up with an effort from just inside the area, which home goalkeeper Ciprian Tatarusanu had to tip around the post at full stretch.
Tatarusanu also had to deal with a threatening corner from Giorgos Karagounis immediately after as Greece looked to stretch their aggregate advantage.
However, the visitors were almost caught on the counter-attack as Bogdan Stancu got on the end of a ball forward before forcing a save from Orestis Karnezis.
Greece responded by picking up the pace and came close to taking the lead after 21 minutes when Georgios Samaras directed a header from a Karagounis free-kick just past the left post.
They were in front just two minutes later, though, with Karagounis supplying another perfect ball into the area which Mitroglou slotted beyond Tatarusanu.
Now holding a 4-1 aggregate lead, Greece began to relax and toy with their opponents, determined to run the legs off the Romanians as they chased the ball around the pitch.
The home side did manage to threaten on occasion but their pressure came to nothing and Karnezis had little to do in the visiting goal.
It was a huge slice of luck which eventually brought the hosts level after 55 minutes.
Romania had again pushed forward but the attack was fizzling out when an attempted clearance from Greece defender Jose Holebas clattered into team-mate Torosidis with the ball rebounding into the top left corner.
The Greek players seemed perplexed by the goal and Romania tried to use this to their advantage as Ovidiu Hoban produced a fierce drive which was palmed away by Karnezis.
Iasmin Latovlevici then fired a 25-yard free-kick over the bar as the home side threatened once more.
The spell of activity continued in the visitors' half as Santos' men were forced to clear a number of corners, with Romania looking to get their noses in front on the night.
But Greece's back-line proved up to the challenge and the final whistle brought both relief and joy for the Mediterranean nation.