Japan profited from Colombia's nightmare start to the World Cup as they secured a victory against 10 men in their Group H opener in Saransk, despite James Rodriguez's late introduction
After the first red card shown at this World Cup - and the second fastest in history at two minutes 56 seconds - Kagawa scored the spot-kick.
Japan should have increased their lead soon after as Takashi Inui and Yuya Osako wasted fine openings.
They were punished when Juan Quintero's clever free-kick, fired low under the jumping wall, brought Jose Pekerman's Colombia on level terms six minutes before the break.
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Colombia had never 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, not having been deemed fit enough to start.
However, it was Japan who regained the lead, Osako finishing with a header from Keisuke Honda's corner.
Rodriguez had been struggling to leave a mark on the game, with Japan
Freed into space after a clever backheel, Rodriguez's blistering strike from inside the box was deflected over the bar by a brave lunge from Osako.
This was the first time Japan had won a World Cup game on European soil, and the first time they had beaten
For Colombia, who reached the quarter-finals in 2014, this was a miserable defeat that leaves them with two very important games against Poland and Senegal to come.