Russia stunned the pundits with a dramatic 4-1 win in Wroclaw, as Poland and Greece drew 1-1.
Initial fears over Ukraine's right-wing "ultra" fans sparking trouble in Poland failed to materialise, as a strong start by the Czechs faded badly.
Alan Dzagoev and Roman Shirokov put Russia 2-0 up at the interval, before Vaclav Pilar notched one up for Czechs.
However, a second from Dazgoev and another from substitute Roman Pavlyuchenko consigned the Czechs to a defeat which not only knocked their confidence for the rest of their group A campaign, but which could have been worse had it not been for Russia's finishing lacking confidence.
Meanwhile, Striker Robert Lewandowski gave Poland a goal in the first half of their opener against Greece, only to see substitute Dimitris Salpigidis equalise in the second half, in a match which saw both teams down to just ten men.
Saturday will see big names Netherlands and Germany open their campaigns when the tournament switches from Poland to Ukraine on Saturday.