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.
A clever back-heel from Arshavin set Yuri Zhirkov free at the byline and his cross found Aleksandr Kerzhakov, but he couldn't direct his side-footed finish on target.
Yet within 60 seconds Russia were in front. Dzagoev capitalised on two Czechs bumping into each other in midfield to surge forwards and release Konstantin Zyryanov down the right. He picked out Kerzhakov at the back post and when his header came back off the upright it was Dzagoev who arrived on the scene in the right place and at the right time to drill home.
Dzagoev then wasted a great chance as he took a wild swing when played in on the right by Kerzhakov. But on 23 minutes it was two as Arshavin played an incisive ball into the box and although it was an inch too far in front of Kerzhakov, Shirokov sneaked in around the back to dink the ball over Petr Cech.
The Czechs produced little in terms of clear-cut chances, but Jan Rezek flicked a header into Vyacheslav Malafeev's arms before sending a weak shot straight at the goalkeeper. Another sweeping Russian move with Shirokov breaking from deep ended with Kerzhakov blazing high over the bar.
The second period began with a strangely muted atmosphere, but seven minutes in it was livened up as Jaroslav Plasil sliced open the Russian defence and Pilar skipped around Malafeev before sliding the ball home.
Arshavin, enjoying one of his more productive games, cleverly clipped in Kerzhakov, but the Zenit St Petersburg striker had not brought his shooting boots to Poland and screwed his effort wide of the far post. His next two efforts were so awful that he was roundly jeered before Advocaat put him out of his misery and brought on Pavlyuchenko instead.
Czech full-back Theodor Gebre Selassie produced a show-reel moment with a spectacular volley into the side-netting and Malafeev got down well to clutch a thumped Tomas Rosicky effort at the second attempt.
But 11 minutes from time Dzagoev effectively sealed the points with a rising finish from Pavlyuchenko's pass. And then Pavlyuchenko added an individual effort from the edge of the box following dogged persistence.