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Steve Clarke’s side, buoyed by a boisterous rendition of Flower of Scotland by the 12,000 inside Hampden Park, started at a frantic pace - with all the action going through captain Andy Robertson down the left.
The hosts could not take advantage of their early dominance, however, and allowed the Czech Republic back into the game.
Robertson remained a threat throughout and drew a save from Tomas Vaclik as he tipped over.
Scotland were making a good account of themselves, but dropped deep and - after a corner - could not clear, to hand the Czechs the opener.
Vladimir Coufal, the West Ham defender, was played in down the right and crossed for Patrik Schick, who guided a fine header into the bottom corner and past David Marshall.
Clarke responded by sending Che Adams on at the break and Scotland were almost level when Jack Hendry curled an effort onto the bar, only for Schick to deliver a stunning sucker-punch moments later.
With the Czechs breaking, Schick spotted Marshall off his line and curling a 50-yeard effort over the head of the keeper for his, and his side’s, second.
Clarke made another four changes but to little avail as Scotland snatched at chances and failed to find their way back in.
It’s England up next on Friday in a do-or-die derby.