Carlos Sanchez was sent off in the third minute of the defeat after he stopped a goal-bound shot with his hand in the penalty box.
Japan goalkeeper Kawashima was called into the action for the first time after Falcao flicked on a shot towards goal from a free kick, and it was easily dealt with.
Yuya Osako's 73rd-minute victor was a huge relief for the Japanese, who were thumped 4-1 by Colombia four years ago during a miserable campaign in which they failed to register a single win. The team joins Mexico, Switzerland and Iceland in earning surprising results.
They could still go through in a very evenly-matched group, but it's already hard to see them replicating their feel-good run in Brazil four years ago.
Jonathan Evans adapted this story based on the Associated Press news report. The referee was quick to send off Sanchez, awarding a penalty to Japan which was converted by Kagawa.
With only the first matches of the group stages concluding today, there have already been more free-kicks scored this summer than in Brazil 2014, and what a collection of goals they have been so far.
"It is just one win, three points, therefore we need to go to the next venue, so we will save our celebration", he said.More news: You won't believe where the cameras are on OPPO's new flagship
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I know Sanchez had a bad game, people need to calm down he usually has jan next to him, also played a lot of games for us last season & he is only 22.
Colombia will also face Poland and Senegal in Group H, but will have to do without Sanchez.
Japan began the second half strongly and eight minutes after the break Kagawa played in Osako, whose shot on the turn was beaten away by Ospina.
Nishino responded by dispatching his own talisman, Honda, from the bench a few minutes later and it was the former AC Milan man who impacted the game first. Ospina gets out well to block, but the rebounds falls directly to the feet of Kagawa, who strokes in the opener. only for Sanchez to hurl himself at it and stop with his arm and chest.
Colombia had never before come back to win a World Cup match in which they had conceded the opening goal - across 10 games - and star player Rodriguez was brought on in the second half, the Bayern Munich attacking midfielder having been deemed not fit enough to start.
"It is tough to lose a player (Sanchez) so early, especially one so important", said Pekerman.
None of Colombia's 19 games at the World Cup have ended goalless.
When the game was due to officially start, Falcao walked across to Japan's side of the field and spoke to referee Damir Skomina in a discussion that lasted beyond the official countdown to kickoff.