The result keeps both nations alive as they remain in the hunt for a second- place finish in Group C, but it also helps Colombia reserve a spot in the knockout round.
Greece, on one point, will conclude its Group C slate on Tuesday against the Ivory Coast at the Estadio Castelao while Japan, also on one point, will finish against first-place Colombia at the Arena Pantanal, also on Tuesday.
The run of play in Thursday's affair was even until the 38th minute when Greece had Kostas Katsouranis sent off for a second caution, which came by way of a sliding challenge on Makoto Hasebe.
But the Greeks almost took the lead shortly after when Vasilis Torosidis took a failed clearance and hammered a shot on goal, but goalkeeper Eiji Kawashima was equal to the task, turning the attempt out of play to deny the Roma man.
Japan had a glorious chance to go in front in the 68th minute when Atsuto Uchida played a square ball across the face of goal, but Yoshito Okubo sent a wayward shot well wide.
Uchida had a chance to give Japan the lead three minutes later when Sokratis Papastathopoulos attempted to clear the ball by dribbling wide, but the Schalke defender turned his first-time effort wide of goal.
The spurned chances indicated that it would not be Japan's day as the Blue Samurai failed to capitalize on playing up a man for over 50 minutes, instead settling for a point to make their meeting with Colombia in the Group C finale a must-win.
2014: The Year in Music [PHOTOS]