Steve Clarke’s side started well before Schick’s fine header converted West Ham full-back Vladimir Coufal’s cross.
And the Bayer Leverkusen star doubled the lead with a phenomenal finish from almost 50 yards out in the second half.
Capitalising on Jack Hendry’s blocked shot as he stepped out from the back, Schick, from just inside the Scotland half, caught David Marshall off his line and curled the ball around the near post and over the goalkeeper’s head to spark wild Czech celebrations.
Scotland soon ran out of ideas despite a valiant late push and will need to respond against England on Friday at Wembley. Here are the player ratings from Hampden Park:
Marshall - 6: Good saves to deny Schick low to his right early and then again shortly after the restart, but he was perhaps guilty of venturing too far out from goal for Schick’s second.
Hanley - 6. Defends near post well and good in the air. Instinct to cover teammates well and extinguish hope of a Czech counter.
Cooper - 5. Struggled for rhythm in the passing game, but did play a gorgeous long ball over the top to find Dykes in behind.
Hendry - 5. Hit the bar with a good curling effort. But a poor decision to strike at goal when stepping out from the back saw him ruthlessly punished. Initially a two on two, Schick shot immediately from deep and produced an unbelievable finish.
O’Donnell - 4. Disappointing distribution coming in off the right. Got in Christie’s way to remove danger after a good run. Can see Schick’s run but doesn’t go early enough to prevent the opener.
Armstrong - 5. Recovers well to drop in when McTominay beaten, good run from deep to cause chaos early in second half, but a scrappy game limited his potential impact.
McGinn - 5. Struggled to get involved with Soucek doing an excellent job on him, but worked hard and won it back well at times.
McTominay - 5: Good dribble into the box and claimed for a penalty, battled well.
Robertson - 7: Great start to the game as his country’s leader, solid at both ends of the pitch. Missed a great chance after being sent in one on one by Christie but was energetic and provided great drive from box to box.
Dykes - 5: Caused problems for the Czech defence in the box, but a poor miss to cut the lead to one.
Christie - 6: Lovely dribble in from the right and then picked out Robertson for a great chance, was substituted at the break.
Che Adams - 6: Caused problems by dropping into space and linking attack and midfield.
Vaclik - 8. Good stop to deny Robertson, even if quite central, stood up well. A great response after Kalas almost chipped him with a poor clearance and then a great save to deny Dykes.
Coufal - 7. Wonderful cross to assist Schick and linked well with Masopust.
Celustka - 6: Coped well with Dykes, embraced the scrappy nature of the Czech game plan.
Kalas - 5: Pulled out wide and beaten for skill by Christie. A mess of a clearance almost put into own net.
Boril - 5: Opened up by Christie early on. Would often smash it clear when he had time to pick out a teammate too.
Soucek - 6: A quiet game in terms of impact on the ball, but he did a job on McGinn and the game suited him in that respect, doing a selfless job for the team.
Kral - 6: Tenacious in the midfield and disrupted any flow to the game for Scotland.
Masopust - 6. Combined well with Coufal to feed Schick down the channel.
Darida - 5. Fierce strike to force Marshall into an early second-half save.
Jankto - 6. Lovely dart to the byline early on and found Schick for a big chance, but a little wasteful despite bright moments.
Schick - 9. Man of the match. Brilliant header to give the visitors the lead, a clean strike early on too, forcing Marshall into a top save at the near post. Then, an absolutely stunning finish from deep to catch Marshall off his line. Missed a glorious chance for the hat-trick.