In a forgettable game in Natal, Japan dominated possession, but were unable to capitalise on Katsouranis’ 38th minute dismissal for a second bookable offence.
The result means both teams still have a chance of qualifying for the last 16 of the World Cup after building on defeats in their opening games.
Japan will meet Colombia in their final group match, with Jose Pekerman’s side now guaranteed a spot in the knockout stages following their earlier win over Ivory Coast.
Greece, meanwhile, have still only scored in one World Cup finals match and must beat Ivory Coast in their last group game to have any chance of progressing.
Japan, who had led against the Ivory Coast before losing 2-1 in Recife, had Cologne forward Yuya Osako in attack, with Manchester United’s Shinji Kagawa among the substitutes.
Greece, beaten 3-0 by Colombia in Belo Horizonte, started with Fulham forward Kostas Mitroglou in attack, backed up by former Celtic frontman Georgios Samaras.
It was a positive start by Japan, with AC Milan's Keisuke Honda, who scored against Ivory Coast, again orchestrating from just behind the central striker.
Greece fashioned an opening on 10 minutes after a positive break from Panagiotis Kone, who tested Japan goalkeeper Eiji Kawashima with a speculative 20-yard drive.
On 20 minutes, Osako almost curled in a fine effort after creating space outside the Greece penalty area.
Japan pressed again when Greece goalkeeper Orestis Karnezis pushed away a dipping free-kick from Honda, before Yoshito Okubo sent a header high over the crossbar.
Greece were forced into a change on 34 minutes when Mitroglou, Fulham's £12million January signing, hobbled off to be replaced by Theofanis Gekas.
Soon, though, Greece were down to 10 men after captain Katsouranis tripped opposite number Makoto Hasebe and, having not long been booked, was shown a second yellow card followed by a red from El Salvador referee Joel Aguilar.
The Greeks then rallied, with full-back Vassilis Torosidis forcing a fine save from the Japan keeper after a low strike from the edge of a crowded penalty area was pushed behind.
There was a tactical change just before half-time when Ioannis Fetfatzidis was replaced by Giorgos Karagounis, the midfielder released by Fulham following their relegation from the Premier League.
Immediately at the restart, Samaras showed some quick thinking to try a lob over the Japan goalkeeper from kick-off, but the ball flew wide.
Samaras, out of contract at Celtic, went into the notebook on 54 minutes when he tripped Okubo to concede a free-kick 25 yards out in the central position. However, Japan substitute Yasuhito Endo struck his shot into the wall.
Kagawa was sent on, in place of Osako, as coach Alberto Zaccheroni looked to freshen up the Japan attack.
Greece went close again as the hour mark approached when a downward header from Gekas was pushed around the post by Kawashima.
On 67 minutes, Kagawa's ball across from the left was right into the path of Okubo arriving at speed at the far post, but he could only drill an angled effort into the side netting.
Southampton full-back Maya Yoshida was also just off target when dashing into the six-yard box as Japan pressed again, feeling they should have been awarded a penalty when Sokratis Papastathopoulos looked to have pushed Okubo in the back.
Karnezis then saved an 18-yard strike from Okubo, before in a rare moment of action at the other end, Samaras glanced a header just wide following a corner.
The Greek keeper pushed away a curling free-kick from Yasuhito Endo as Japan were left frustrated.
The final round of Group C matches sees Japan take on leaders Colombia in Cuiaba needing to win to stand a chance of progress, while Greece play Ivory Coast at Fortaleza also needing other results to go their way.