Ladislav Krejčí opened the scoring for the Czech Republic in the first minute of the game in Prague, and Tomáš Čvančara added another goal two minutes later.
Jan Kuchta put the home team 3-0 up in the 64th minute.
Midfielder Damian Szymański scored a consolation goal for Poland from close range in the 87th.
The Poles, captained by star striker Robert Lewandowski and coached by Portuguese manager Fernando Santos, take on Albania in their next Euro 2024 qualifier in Warsaw on Monday.