Fernando Santos' side missed out on automatic qualification for next year's tournament in Brazil on goal difference after finishing level on points with Bosnia-Herzegovina in Group G.
Greece should head into the first leg at Georgios Karaiskakis Stadium in Piraeus with plenty of confidence, though, having won their last six games without conceding a goal.
The 2004 European champions won eight of their 10 qualifiers and conceded only four goals in the process, amassing more points than any other second-placed side in the European qualifying groups.
However, Greece, who are ranked 15th in the world, will be without Kyriakos Papadopoulos against Romania as the Schalke defender continues to struggle with a knee injury.
Konyaspor striker Fanis Gekas, 33, has been recalled by Santos in an experienced squad that also includes skipper Giorgos Karagounis, 36, and 34-year-old midfielder Costas Katsouranis.
Greece have appeared in just two World Cup finals, the second of which was in South Africa three years ago.
Romania have not featured in the finals since the 1998 showpiece in France, but they kept their hopes of reaching Brazil alive by securing a play-off place in Group D.
Victor Piturca's side finished nine points behind runaway pool winners the Netherlands, but did enough to end two and three points above Hungary and Turkey.
They will be without captain Vlad Chiriches after the defender suffered a broken nose playing for Tottenham against Newcastle in the Premier League, but Piturca is hopeful the side can cope without the centre-back.
"Chiriches is very important for us, not only because he's our captain. But as I said many times, no team is dependent on only one player," he said.
Striker Adrian Mutu, Romania's joint-leading record goalscorer, was omitted from Piturca's squad, but the likes of Getafe striker Ciprian Marica and Genclerbirligi forward Bogdan Stancu will provide an attacking threat.
Meanwhile, Manchester City goalkeeper Costel Pantilimon was called up after Ciprian Tatarusanu injured his back in training.
First-choice keeper Tatarusanu remained with the squad, though, and could feature on Friday.
