Japanese striker Osako after beating the Colombian backline, launched a shot straight into David Ospina, who could only manage to send it back to Kagawa who struck on the rebound which was blocked by Sanchez with his hand.
The ball went out Kagawa and his goal-bound follow-up hit the outstretched arm of Sanchez, drawing an immediate red from referee Damir Skomina.
Colombia equalised six minutes before the interval when Juan Quintero's low free kick squeezed over the line.
This is the first World Cup tournament in which as many as four South American teams have failed to win their opening game since 1974.
Japan's victory over group-favourites Colombia has resulted in a first ever victory for an Asian side against a South American team during the World Cup.
Perhaps sensing a chance to steal the match, Colombia coach Jose Pekerman sent on James Rodriguez in the 59th minute, the 2014 World Cup's golden boot victor having been questionable before the match due to a calf injury.
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Their next game is against South Korea on Saturday 23 June, and then against Sweden on Wednesday 27 June. Mexico's fans celebrate victory of their team after the match.
It was the second-fastest red card in World Cup finals history, bettered only by the 52 seconds it took Jose Batista of Uruguay to be sent off against Scotland at Mexico '86.
"If we had actually won the World Cup, we would have had a parade on the main street of Saransk", Japan coach Akira Nishino said.
Although Colombia had looked much better in the second half after their earlier tactical substitution, they could only hold on for so long, as Yuya Osako powered home a header from a corner to put his side ahead with 20 minutes to play. He almost single-handedly guided Colombia into the championship by scoring six goals in only five games.
The first red card of the tournament was produced in the opening exchanges, with Sanchez given his marching orders for denying a clear goalscoring opportunity.
It was also sweet revenge for Japan, who were thumped 4-1 by the same opponents in Brazil 2014, but they wasted plenty of chances to kill the game off earlier.
With just three minutes on the clock, Colombia were forced to play the majority of the match with ten men, and it cost them dearly.
Japan, 45 places below their opponents in the latest Federation Internationale de Football Association rankings, had to fend off one final attack from Los Cafeteros as James's shot from eight yards was superbly blocked behind by matchwinner Osako.