The Samurai Blue were aided by the second-quickest ever red card shown at the finals, as Carlos Sanchez was dismissed inside the opening three minutes for a handball inside the box.
After a frantic first half, the game slowed in the second but Osako burst into the Colombia box and drew a save from David Ospina with a tricky close-range shot that the Arsenal goalkeeper parried away.
Coach Akira Nishino's plans worked to perfection as Samurai Blue got just the result they were hoping for.
With Colombia ranked 16th in the world and Japan 61st, the South Americans were expected to win. Los Cafeteros were made to suffer by their opponents in the second half, however, and having endured the toughest of starts Falcao and Co now have to ponder their approach to their next two matches.
This was the first time Japan had won a World Cup game on European soil, and the first time they had beaten a side from South America at the tournament.
Hiroki Sakai should have restored Japan's lead when his low cross from the right was played back to him by Osako, only for the full-back to drill the ball at Oscar Murillo, with the deflection taking the effort wide.
Both Senegal and Poland - who meet later today - will fancy their chances of qualifying from this group which, with four teams committed to attack, looks like being a thriller.
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In previous defeats, Egypt's national team and coach have often scrambled to respond to criticism. Uruguay also has three points while Egypt and Saudi Arabia have none.
"Right now our pain is precisely because after that huge effort after scoring that goal. we lost because we were worn down, we were exhausted and even if I tried subbing on a couple of fresh players it was very hard for us to recover possession and Japan had its opportunities", Pekerman said.
"To score a goal at the World Cup has been a dream for me since I was little, so I was extremely happy", said the match-winner.
"Our players were aggressive from the start and I think that worked very well for us".
The midfielder, who was the leading scorer at the World Cup four years ago with six goals in five games, missed training on Friday with muscle fatigue. Unsure on the ball, erratic passer and not good reader of the game.
Okazaki did get in the game, but not until the 85th minute.
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.
He came on in the 59th minute, but his best chances were thwarted by Japan's desperate defending. "I wanted to play along the sides so that they could pass balls forward so that we could cause Japan more problems", said Pekerman. The 32-year-old sent his corner from the left side curling and dipping past the Colombia defenders into the path of the flying Osako.