The 40,000 crowd packed into the stadium in the southern city of Wroclaw observed a minute's silence for the victims of Friday's Paris attacks with both teams wearing black armbands.
Despite fielding a team without established players like Bayern Munich's Robert Lewandowski or Sevilla's Grzegorz Krychowiak, Poland's young attackers had their side in the lead in only the third minute.
Teenager Bartosz Kapustka led a quick charge from the left side and fed 21-year old Arek Milik, who scored with a brilliant header.
Milik was involved again in the 12th minute, with an assist after a corner for another headed goal, by midfielder Tomasz Jodlowiec.
The Czechs regained some confidence towards the end of the first half, Vladislav Krejci scoring in 40th minute as he took advantage of a misplaced pass by Poland's Tomasz Jodlowiec.
Poland's third goal came in the 70th minute. Milik, instead of trying to score in a one-on-one duel against Petr Cech, unselfishly passed to Kamil Grosicki, who had no problems in finding the empty net.
Grosicki, who plays for a French team Stade Rennais, showed an undershirt with a picture of the Eiffel Tower, the French flag and a message that read "Pray for Paris".
(Reporting by Jakub Iglewski; editing by Ken Ferris and Steve Tongue)
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