Slovakia had squandered a slew of chances before the 22-year-old Roma forward broke the deadlock in the 76th minute when he headed into the top corner from captain Borek Dockal's cross.
The goal came minutes after Schick had replaced Michael Krmencik, who scored the first goal of the match after 52 minutes when he held off a marker and side-footed home after a neat throughball from Dockal.
Slovakia responded minutes later when Marek Hamsik, who was winning his record 108th cap, smashed a rebound into an empty goal after Czech Republic goalkeeper Tomas Vaclik did well to save an Adam Nemec header after a corner.
All the goals came after an even opening half in which Slovakia controlled possession but Czech Republic had the best chance when Matej Vydra's volley from the edge of the box was cleared on to the post in the ninth minute.
The League B Group 1 match also marked former national team assistant Jaroslav Silhavy's first game in charge of Czech Republic since replacing Karel Jarolim after the team's 5-1 defeat to Russia in a friendly in September.
Ukraine top the group after beating Slovakia 1-0 at home and coming from behind to snatch a 2-1 victory in the dying seconds over the Czech Republic away.