A win for either team in Natal would have taken them level on points with the Africans with the final round of matches to play, and piled the pressure on Yaya Toure and co.
But Japan were left ruing missed chance after missed chance against the 2004 European champions.
Greece were awful in their opening game defeat to Colombia, and they were little better against the Japanese.
They weren’t helped by the actions of their captain, Konstantinos Katsouranis, who contrived to get himself sent off after 38 minutes for two bookable offences, the second of which, for a crude lunge, came just 12 minutes after his first. That’s leadership for you!
But Japan failed to make their numerical advantage count as they missed a string of excellent opportunities.
Yuya Osako had come close on a couple of occasions in the first period, but those chances were nothing compared to the ones they squandered in the second.
Yoshito Okubo will still be wondering how he missed in the 68th minute when, arriving at the far post with an empty net gaping in front of him, he smashed the ball over the bar and into the crowd.
And that was followed three minutes later by Atsuto Uchida - who became Japan's youngest World Cup scorer in a 2008 qualifier – who slid the ball wide of the post after more dreadful defending by the Greeks.
Greece, for their part, did fashion one chance in the second half, but Theofanis Gekas saw his header saved by Japanese Eiji Kawashima.
Had that got in and stolen the points for the Greeks, however, it would have been akin to daylight robbery.
Their involvement at Brazil 2014 will likely end on Tuesday against Ivory Coast, and very few people outside Greece will mourn their departure.
As for Japan, they now need to beat Colombia and hope the Greeks do them a favour against the Africans in Fortaleza.
But, after two games, one point and no goals so far from Alberto Zaccheroni's man, there won't be much money bet on that.
