Colombia equalized late in the first half on Juan Quintero's rolling but accurate free kick, which sneaked inside the right post.
Japan will try to claim revenge for their 4-1 drubbing at the hands of Colombia, who reached the quarter-finals, in their final group game at the 2014 World Cup finals.
Japan continue their quest for qualification from Group H when they travel to the Central Stadium in Yekaterinburg to face Senegal on Sunday (4pm BST kick-off).
Osako broke clear and, although his initial effort was parried by David Ospina, Kagawa's follow-up effort was goalbound until Sanchez stuck out an arm.
A Sweden supporter holds up a scarf ahead of a World Cup Group F match between Sweden and South Korea on June 18, 2018.
But a brilliant free kick has Los Cafeteros level. Get live score of the FIFA World Cup 2018 match between Colombia and Japan here.
With 20 minutes to go, Japan took off Kagawa and brought on Keisuke Honda, with Bacca coming on for Colombia in place of Jose Izquierdo.
His sending-off in the third minute, for a deliberate handball, was the second fastest in World Cup history after Uruguay's Jose Batista was dismissed after 55 seconds against Scotland in 1986.
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Although we ended up with 3 goals, there were frequent breaks in play. "I'm going away with 23 of my brothers, so we all get on well".
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. Kagawa eventually dispatched the penalty.
Barrios was booked for a foul on Kagawa, and then Inui threatened again before his shot, after cutting inside, was blocked by a defender.
Japan started the game on an exciting note, pressing heavily from the word go as they had a shot at goal inside the first couple of minutes.
The 29-year old was a key player in Japan's qualification run scoring six goals and will have to be at his best against the South Americans if Japan has a chance of getting out of Group H.
"From the start I thought we could be very aggressive and of course we had the advantage of more players", Nishino told reporters.
Despite the numerical disadvantage, Colombia gained a foothold in the game and were awarded a free-kick on the edge of the area in the 38th minute after Falcao was bundled over by Yoshida.
James Rodriguez was left out of Colombia's starting line-up for their opening World Cup match against Japan on Tuesday as the Brazil 2014 top scorer labours with a calf strain.
Moments later, Skomina ordered both teams to change sides, after which the match began.
