Kagawa stepped up to slot the subsequent penalty, which was the start of action-packed first-half.
Japan's midfielder Shinji Kagawa (L) vies with Colombia's midfielder Carlos Sanchez during the Russian Federation 2018 World Cup Group H football match between Colombia and Japan at the Mordovia Arena in Saransk on Jun 19, 2018.
Shinji Kagawa got the Samurai Blue off to a dream start when he converted a penalty after six minutes, but a Juan Quintero freekick saw Colombia pull level six minutes before the break.
Not only was Osako instrumental in both goals, he sprawled to block a close-range shot by Colombia midfielder James Rodriguez in the waning minutes.
Battling for every ball, Colombia captain Radamel Falcao earned the free-kick from which Juan Quintero equalised before half-time.
Japan will next face Senegal on Sunday (Monday NZT) in Yekaterinburg, while Colombia takes on Poland in Kazan on the same day.
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.
This is the first World Cup at which four South American nations have failed to win their first game since 1974.
Back to the red card theme, and Sanchez became the second-fastest player to be sent off in a World Cup.
Japan dominated the second half, creating a series of chances before Yuya Osako headed in the victor from a set-piece.
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.
"We had practiced loads of set pieces and that goal was straight off the training ground", said Osako.
Japan upset 10-man Colombia 2-1 in a dramatic match on Tuesday to become the first Asian side to beat South American opponents at the World Cup.
"To lose one player in the three minutes to lose such a crucial player, is not an easy thing", Colombia's Argentine coach Jose Pekerman told reporters. He almost single-handedly guided Colombia into the championship by scoring six goals in only five games.
Despite playing with a man down, Colombia did not let their heads drop as they strived to get back into the game after the setback.
There was some confusion about why the incident justified a red card.
Earlier, Colombia's star midfielder James Rodriguez, the top goal scorer of the 2014 World Cup, has been brought into the match against Japan after 59 minutes.