Few neutral pundits give the Romanians much hope of qualifying for next year's tournament in Brazil, saying the team need to iron out defensive lapses, particularly in set pieces.
Piturca knows his men have to switch from their usual no-risk approach to a straightforward playing style and be more efficient in front of goal if they are to score at least twice.
"If we manage to qualify, it will be extraordinary for Romanian football, and for myself," said Piturca, who has been criticised at home for been overly tactical.
Romania have not qualified for the last three World Cups and the 57-year-old coach misfired in his attempts to get them to the finals in 2006 and 2010.
"It's our last chance and we must do everything possible to play better and win by two or more goals and fulfil our dream," said West Ham United defender Razvan Rat.
First-choice keeper Ciprian Tatarusanu could be fit for the match at the National Arena after recovering from a back injury and would replace veteran Bogdan Lobont, who made his first appearance this season in Athens.
Piturca also hopes to have captain Vlad Chiriches back after the Tottenham Hotspur centre back received permission to play with a face mask protecting his fractured nose.
The 23-year-old suffered the injury during his team's 1-0 Premier League loss to Newcastle United earlier in the month.
However, Romania will be without suspended holding midfielders Alexandru Bourceanu and Costin Lazar.
Bogdan Stancu scored in the first half at the Georgios Karaiskakis Stadium, for the first goal Greece have conceded since March 22, but home fans will want to see striker Ciprian Marica, with 24 goals in 67 internationals, at his sharpest.
"The stadium will be full and the pressure will be on the Greeks. Nothing is impossible," said Marica, who - after being Romania's sole striker in Athens - is expected to partner Marius Niculae in attack with Piturca opting for a more orthodox 4-4-2 formation.
Greece coach Fernando Santos has sounded a note of caution ahead of the match and called on his players not to lose concentration as they go in search of a place in the World Cup finals for only the third time.
"Although we are ahead in the tie we still need to go to Romania with a focused mind-set as everything will be decided then; nothing is over yet," he said.
"We are at halftime in the tie so there is still plenty of work to do and we'll have to show the same appetite and concentration in the second leg so we don't throw away what we have built on in Athens.
"While I will not forget that we have the advantage, we must not take too many risks. Our focus will be to keep a clean sheet because if we concede an early goal it will create problems for us."
The 59-year-old Portuguese is set to make only one change to the team which performed so impressively in the first leg.
Andreas Samaris or Giorgos Karagounis will replace captain Kostas Katsouranis, who is suspended after collecting three yellow cards, in the Greeks' three-man midfield alongside Alexandros Tziolis and Giannis Maniatis.
While Santos will not confirm who will start, Fulham midfielder Karagounis, Greece's most-capped player with 130, is likely to get the nod due to his experience.
Greece will again look to in-form Olympiakos Piraeus striker Mitroglou to provide the goal threat at the head of their attack with Celtic's Giorgos Samaras and PAOK Salonica's Salpingidis supporting from the flanks.