Danish players are now dreaming of a repeat of 1992 when Denmark won the European Championship despite not even qualifying.
Netherlands central defender Matthijs de Ligt was sent off for a handball in the 55th minute when under pressure from Schick.
Schick was awarded the penalty after being elbowed in the face by Croatia defender Dejan Lovren while both challenged for the ball in the air.
Schick ran onto a rebound just inside the Scotland half, saw goalkeeper David Marshall way out off his line and let fly.
Czech striker Patrik Schick picked up the ball as it bounced off a team-mate after a shot by Jack Hendry, catching Marshall well off his line to score from just inside the Scottish half.
The Czech Republic silenced a 12,000 crowd at Hampden on Monday with a 2-0 win thanks to two goals and one moment of magic from Patrik Schick that will live long in the memory.