After lengthy protests, Sanchez eventually left the field and Kagawa was allowed to slot the penalty clinically into the bottom right corner of the net and Colombia's game plan was in tatters.
Kawashima's error then gifted Colombia an equaliser, with Quintero's low free-kick creeping over the line at the near post after Falcao was brought down on the edge of the area.
Japan became the latest team to pull off an upset at the World Cup.
In a last throw of the dice, Pekerman introduced James Rodriguez, who did not start due to a calf problem, in the 59th minute but the Golden Boot victor in Brazil was unable to change the course of the match.
Victory for the Samurai Blue is their first ever on European soil at the World Cup and their first against South American opposition in the competition.
Colombia simply could not get out, and it was no surprise whatsoever when Osako scored what proved to be the victor, heading home a corner taken by the substitute, Keisuke Honda.
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After Quintero slotted home a clever free-kick against the above 'keeper Kawashima, it resulted in more free-kicks being scored in this World Cup than in the entire Brazil tournament four years ago.
In the early minutes of the game, there was controversial drama as Carlos Sanchez was handed the first red card of the tournament for stopping a goal-bound shot of Shinji Kagawa with a raised arm in the box.
"We had practiced loads of set pieces and that goal was straight off the training ground", said Osako.
There was some confusion about why the incident justified a red card.
With his side struggling to get a grip on the game, Jose Pekerman sent on a half-fit Rodriguez for the final half an hour to no avail.
Japan are the first Asian side to beat a South American side at a World Cup.
Los Cafeteros impressed at the 2010 competition, reaching the quarterfinals whilst playmaker James Rodríguez picked up the golden boot in the tournament.
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.