FC Midtjylland's U19 team otherwise led at the break after 17-year-old Julius Emefile intercepted a poor pass from the visitors' keeper Oliver Whatmuff to give the unsung Danes the lead after 41 minutes of play.
However, the visitors took only litte time to respond in the second half when Manchester City's Lakyle Samuel was left completely unmarked to steer home a close-range header and restore parity.
15 minutes from the end, Manchester City were reduced to ten men as Charlie Gray received his second yellow card in the game and shortly afterwards the 19-year old Jaden Heskey scored in his own net as he was trying to clear a delivery from FC Midtjyllands' Mathis Konradsen.
But nine minutes from the end Matthew Warhurst latched on to a pass from Max Alleyne to make it 2-2 which meant the match had to be decided by penalties.
And as FC Midtjyllands Malik Pimpong was the only one not to convert from the penalty spot, Manchester City booked their ticket for the next round of the tournament.