Victor Piturca's men have a two-goal deficit to overturn in Bucharest but they will take heart from the fact that they have won five of their last seven in their own backyard
In the past 12 months, the Romanians have won five out of seven encounters on home soil, beating the likes of Belgium and Australia, both of whom will be at next year's tournament in Brazil.
A double from Konstantinos Mitroglou sandwiched an effort from Dimitris Salpingidis in Athens on Friday, with Romania's away goal - which could prove crucial - coming courtesy of Bogdan Stancu.
Indeed, Romania have kept three clean sheets in their last five matches in Bucharest and Salpingidis is anticipating a tough test on Tuesday.
"Of course, in theory, we have the best chance to qualify, especially after we won the first match with a two-goal difference," said the Greece forward.
"However, the distance between winning and losing is very small, especially in big football games.
"We have to be careful in Bucharest; we have an extremely difficult mission there."
Greece coach Fernando Santos has led his side to seven consecutive victories and they have only suffered defeat once in 15 matches.
Santos will hope Mitroglou continues his rich vein of goalscoring form, which has seen the 25-year-old score seven times in as many appearances for club and country.
The Olympiacos striker was the star performer in the first leg and the Romanian defence was unable to keep him under control.
Victor Piturca is without his captain Vlad Chiriches due to the defender's broken nose.
Both sides have a player suspended for the match, although Romania may not miss midfielder Alexandru Bourceanu as much as the visitors will miss captain Kostas Katsouranis.