The referee was quick to send off Sanchez, awarding a penalty to Japan which was converted by Kagawa.
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. Falcao captain's Colombia in his first World Cup appearance.
Colombia will also face Poland and Senegal in Group H, but will have to do without Sanchez.
Pekerman brought on 2014 World Cup Golden Boot victor James Rodriguez in the second half but the Bayern Munich star, not fully recovered from a calf injury, was not allowed much of the ball by a disciplined, energetic Japan side.
Japan looked threatening on the counter during the rest of the first half, as the South Americans struggled to deal with playing a man down in midfield and failed to track back to defend.
The fastest-ever though still remains Jose Batista, who was sent off inside the first minute for fouling Gordon Strachan in 1986 World Cup match between Scotland and Uruguay.
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Japan dominated the second half, creating a series of chances before Yuya Osako headed in the victor from a set-piece.
The moment which settled the match came on three minutes, when an error from Davinson Sanchez allowed Yuga Osako in on goal.
A costly mistake by Colombia midfielder Carlos Sanchez in the opening minutes led to a red card and a penalty, helping Japan take an early lead.
Japan started the game on an exciting note, pressing heavily from the word go as they had a shot at goal inside the first couple of minutes. Instead, Japan eked out a 2-1 victory over Colombia, which played with 10 men after a Carlos Sanchez handball in the box in the third minute.
Might wonder if he could have dealt with the corner for Japan's second goal, when he initially came off his line before retreating.
Just before half time, Colombia were handed a dubious free kick in front of goal.
Colombia soundly defeated Japan 4-1 when the sides met in group play in Brazil four years ago, and the Japanese also began the game without Okazaki, a Leicester forward who has been trying to overcome a sore calf and was replaced in the starting lineup by Osako.
Jose Izquierdo 5 - Saw his impact nullified after Colombia went down to ten men, although he could have done better to get in the game.