They were heading out when Bednarek scored, and Southampton's Maya Yoshida headed just wide on 72 minutes as they pushed for an equaliser.
Poland are out of the tournament after two defeats, and they will have nothing more to play for other than pride.
If this game ends in a draw then Belgium and England will finish with identical group stage records, so the group winners will be determined by fair play points (England has a one yellow card advantage before kick off) or if that's level then it will be a random draw. The Japanese players slowed play down to nearly nothing, softly passing the ball back and forth in little triangles in their own end to waste time.
"I decided that I was going to rely on the other match's result", he told reporters.
Poland entered this tournament as the 8th ranked team in the World with predictions of topping a relatively weaker Group H consisting Senegal, Japan, and Colombia, with Colombia said to be there closest rivals for their chase for the top spot.
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US decision that upheld the detention of Japanese-Americans during World War II. "Wow!" he tweeted just minutes after the ruling. Instead, he said, they had to send notice to USA officials in Washington so they could decide to deny or grant the waiver.
Germany crash out as Korea Republic end on high
Defending champions Germany have been eliminated from the 2018 World Cup after losing to South Korea in Kazan . With Germany desperately looking for a goal to get back in the match, Neuer joined the attack.
Germany to change tactics for match against South Korea
Carlos Vela, meanwhile, scored last time out and has generally been effective for Mexico if not a tad wasteful in front of goal . Sweden have impressed me greatly and although Mexico beat Germany , I still have doubts over the North American side.
Japan has a tough final group-stage game against Poland, which despite being 0-2-0 through two games still is a quality opponent with a world-class striker in Robert Lewandowski.
Neither Japan nor Poland made an effort to win the match after hearing about Mina's goal over in Samara.
"It was for us more important for us to get into the next round than to win the match, " Japan midfielder Gotoku Sakai said.
Still, Japanese fans were left toasting goalkeeper Eiji Kawashima, who in the first half made a spectacular save that denied Kamil Grosicki's header and also prevented a Japanese own goal after the break.
Then, with nine minutes remaining, Tomoaki Makino - in an attempt to intercept another risky cross by Grosicki - could only send the ball towards his own goal but Kawashima reacted well to make the save.
Japan will go on to face the victor of the Belgium v England match in the Round of 16.