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Harry Kane opened the score in the match from penalty on 57 minutes, but Colombia defender Yerry Mina snatched a dramatic stoppage-time equaliser to force extra time.
The extra-time ended with the game level at 1-1.
England blinked first in the penalty shootout with Jordan Henderson seeing his effort saved by David Ospina, but Colombia missed the next two - Mateus Uribe hit the bar before Carlos Bacca saw his penalty saved.
Sweden earlier beat Switzerland 1-0 in their last 16 game to advance.