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 showreel 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.
In Image: Russia's Roman Shirokov kicks the ball past Czech goalkeeper Petr Cech and Michal Kadlec to score a goal