Alberto Zaccheroni's men played with a numerical advantage for most of the game following Kostas Katsouranis' dismissal but could failed to break the deadlock.
Greece held on for a goalless draw against Japan in Natal on Thursday, ensuring Colombia will play in the round of 16 in Brazil.
Despite playing the entire second half with a numerical disadvantage after skipper Kostas Katsouranis was expelled seven minutes before halftime, Greece denied the misfiring Japanese at the Arena das Dunas as both teams picked up their first points of the World Cup.
Katsouranis went into the book for the first time in the 27th minute when he slid into the back of Yuya Osako and his trip to halt Japan captain Makoto Hasebe's break 11 minutes later was the end of his match.
The draw saw Colombia, which had defeated Ivory Coast 2-1 earlier on Thursday, secure a berth in the knockout stages at its first World Cup since 1998, as it leads Group C with six points with one game to play.
The most intriguing selection for Greece was that coach Fernando Santos stuck with Giannis Maniatis despite the Olympiacos defensive midfielder having threatened to leave Brazil on Wednesday after a training ground argument.
Maniatis retained his spot in defensive midfield, while Kostas Mitroglou and Ioannis Fetfatzidis replaced Theofanis Gekas and Dimitris Salpigidis respectively.
Japan coach Alberto Zaccheroni made the brave decision of dropping Shinji Kagawa for Yoshito Okubo, while Yasuyuki Konno took Masato Morishige's spot in central defense.
Kagawa had been largely invisible against Ivory Coast but the sight of him on the bench at the Arena das Dunas was still a shock, with the playmaker having started all but one of his country's last 12 matches.
Both teams had pledged to attack in Natal after losing their opening games of the World Cup but 10 minutes passed before the first genuine chance was created; Panagiotis Kone driving through midfield before shooting powerfully straight at Eiji Kawashima.
Japan had over 75 percent possession in the first half but generally struggled to test Orestis Karnezis with Okubo shooting tamely at Greece's goalkeeper and curling another effort wide either side of the 20-minute mark, before the game changed in the 38th minute, when Katsouranis was sent off.
With his team down to 10, Santos made two changes before halftime, sacrificing Fetfatzidis and Mitroglou for Giorgos Karagounis and Gekas respectively.
At the break, Zaccheroni brought on Yasuhito Endo for Hasebe in a bid to insert some creativity into Japan's lineup, before Kagawa was recalled in the 57th minute at the expense of Osako.
But despite the two substitutions, Japan still struggled to break down Greece's stubborn defense.
The Asian nation bombarded Greece's goal, with Okubo wasting the best chance when he blazed wide in the 68th minute, but the Europeans desperately held on to frustrate Zaccheroni's side and leave both teams needing a win in their final game to advance from Group C.