Alan Dzagoev notched a brace with Roman Shirokov and Roman Pavlyuchenko grabbing one each as Russia went two points clear at the top of the group following the earlier 1-1 draw between co-hosts Poland and Greece.
It was a statement of intent from a team many are starting to regard as more than just outsiders for overall victory.
For the Czechs though, Vaclav Pilar's strike was scant consolation from a poor showing.
Russia seemed disjointed at the beginning and it was the Czechs who bossed the opening exchanges as Dick Advocaat's team struggled to find their rhythm.
But once they did, they carved Michal Bilek's team open in ruthless fashion.
In Image: Russia's Alan Dzagoyev, center, is congratulated by teammates after scoring his side's third goal during the Euro 2012 soccer championship Group A match between Russia and Czech Republic in Wroclaw, Poland, Friday, June 8, 2012.