Schick joined Cristiano Ronaldo at the top of the scoring charts with his fifth goal of the tournament early in the second half in Baku.
Yet he will have no further opportunity to add to his tally, as a fantastic first-half performance, which included goals from Thomas Delaney and Kasper Dolberg, ensured Denmark reached the last four of a European championship for the first time since it won the 1992 tournament.
Kasper Hjulmand's team, whose tally of 11 goals trails only fellow semi-finalist Spain, will face England after it thrashed Ukraine 4-0 in their quarter-final clash in Rome.
Approximately 1500 Danish supporters were able to make the trip to Baku, and they were celebrating within five minutes.
Jens Stryger Larsen's corner – which should not have been awarded – found Delaney unmarked, and the Borussia Dortmund midfielder made no mistake with a brilliant header.
On his 21st birthday, Mikkel Damsgaard just failed to squeeze a finish beyond Tomas Vaclik from a tight angle, before Stryger Larsen and Delaney combined for another chance – the latter scuffing wide.
Dolberg made no such mistake three minutes before half-time, however, as he cushioned home from Joakim Maehle's exquisite, outside-of-the-foot cross from the left.
Antonin Barak drew a fine save out of Kasper Schmeichel after the restart, with Simon Kjaer then getting a vital block on Schick's overhead kick.
Yet the Czech Republic's pressure told in the 49th minute – Schick placing a measured first-time finish into the bottom-left corner after being found by Vladimir Coufal.
Tomas Soucek made a brave block to deny Yussuf Poulsen just after the hour, though the Czechs were dealt a blow when Ondrej Celustka succumbed to injury.
Poulsen was let off the hook for another miss when Kjaer cleared in front of a gaping goal soon after, and with Schick going off with an apparent injury late on, Denmark held firm to book their spot at Wembley.
This was the third meeting between Czech Republic and Denmark at the European championships – the Czechs had won both previous games, 2-0 in the UEFA Euro 2000 group stages and 3-0 in the 2004 quarter-final.
But Denmark was in inspired form in the first half to gain revenge in the sweetest of fashion, and the pre-tournament dark horses – shorn of course of their standout player in Christian Eriksen – will be dreaming of replicating that 1992 triumph.