Japan received two fewer yellow cards (four) in the group stage, while Senegal had six yellow cards.
Colombia have three points while Poland can not advance after losing their first two games.
Senegal need just a point to secure their progress to the last 16, following an opening 2-1 win over Poland and a subsequent 2-2 draw against Japan.
But after Japan also lost to Poland, 1-0, Japan and Senegal remained deadlocked in second place in the group at four points each, meaning that advancing would come down to tiebreakers.
Poland's Jan Bednarek scored the only goal of the match in the 59th minute.More news: Putin summit is on; details Thursday
Japan will play the winners of Group G - either England or Belgium, who were to play later Thursday - in the next round.
It is they that will kick on to the knockout stages of the World Cup, despite finishing their group with an identical points and goals tally to Senegal, who'll be on a plane home in the next 48 hours.
In a insane, unforeseen tiebreaker, Japan finished with four points just like Senegal.
Heading into the final day of the group stage, three teams - Japan, Colombia, and Senegal - are all still in control of their destinies as they battle for two spots up for grabs in the knockout round.
"I fancy Colombia [advancing] after that performance [against Poland] - I thought they were absolutely brilliant and I like Senegal as well, but I just feel like Colombia had that horror moment in their first match getting a red card and losing that match [against Japan] and now they have a lot of momentum", TSN soccer analyst Steven Caldwell said. That resulted in the rarely-used fair play rule to determine which team advanced.