Juan Fernando Quintero will start for James, who is technically available from the bench, against Japan.
Japanese pressure paid off when Osako, who was a constant menace to the Colombia defence, leapt highest from a corner and guided his header in off the post with 17 minutes to go.
Asian teams had managed three draws in 17 matches against South American sides but the four-times Asian champions made their extra man count after Colombia midfielder Carlos Sanchez became the first player to get a red card in Russian Federation.
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.
Referee Damir Skomina didn't hesitate in brandishing the first red card of this World Cup - the second fastest in the tournament's history - and Kagawa showed composure to handle the long delay and send the Arsenal goalkeeper the wrong way.
Yuya Osako headed home the winning goal in the 73rd minute
So Sanchez's right arm movement sent Japan to the spot. But Rodriguez had been laboring with a sore left calf recently, casting doubt over his readiness to play.
Radamel Falcao is set to lead his side out against Japan on Tuesday afternoon, in what will be his first World Cup game at the age of 32.
In Jose Perkerman, Colombia has an experienced tactician who is no stranger to managing at the World Cup having let his native Argentina in 2010 and Colombia to their best ever finish in 2014. With the "Fubo Premier" bundle, you will get access to all four of the World Cup soccer TV channels in most markets.
Colombia will also face Poland and Senegal in Group H, but will have to do without Sanchez.
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.
Colombia can win out - something they're capable of.
Willian a £60m target for Manchester United?
Leeds United have missed out on the signing of Manchester United stopper Dean Henderson after he joined Sheffield United on loan. But Crystal Palace also have reason to believe they have a good chance of signing the Arsenal academy graduate this summer too.