Osako's gritty determination led to a 73rd-minute header from Keisuke Honda's corner kick that gave Japan three points in Group H.
Colombia, which played with 10 men for the rest of the match, scored late in the first half on Juan Quintero's rolling but accurate free kick, which sneaked inside the right post.
Japan have opened their 2018 World Cup campaign with a 2-1 win against 10-man Colombia at the Mordovia Arena this afternoon.
Brazil 2014 Golden Boot victor James Rodriguez came on for the last half-hour after labouring in training with a calf strain but could not inspire his team to pull back on level terms.
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.
Akira Nishino's men came into the tournament as one of the lowest ranked teams but they defied their position by making good use of their man advantage and fully deserved to have their lead restored when FC Koln forward Yuya Osako headed the victor in the 73rd minute.
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Incredibly, moments later Samuel Umtiti stuck up a fist to flick on an Australian free kick and gift them a penalty. Giroud and midfielder Blaise Matuidi had a big impact after coming in as substitutes during the second half.
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The news comes as a blow to Colombians, who will have fresh memories of what Rodriguez did on the World Cup stage four years ago.
Okazaki did get in the game, but not until the 85th minute.
Sanchez handled the ball to stop Shinji Kagawa's goal-bound attempt, and the referee had no hesitation in brandishing the red card and pointing to the penalty spot. I'm not sure a red card is needed as well as a penalty, and nor is he - it takes him a long old time to depart.
Might wonder if he could have dealt with the corner for Japan's second goal, when he initially came off his line before retreating.
Osako's 73rd-minute victor meant the Japanese avenged their 4-1 mauling in the group stages of Brazil 2014 as Colombia played with a man down for 86 minutes in Saransk.
In what what was a frantic opening, Colombia responded in positive fashion with Radamel Falcao going close in the 12th minute when he got on the end of a Quintero free-kick, only to be denied by Kawashima in the Japan goal.