Andrei Arshavin, playing his first game of the tournament after suspension, inspired a superb attacking display.
He was involved as Aleksandr Anyukov set up Roman Pavlyuchenko for a close-range finish after 24 minutes.
And Arshavin then started and finished a sweeping move to slide home Yuri Zhirkov's pass in the 50th minute.
Russia exerted almost total domination and also struck the woodwork through Pavlyuchenko and Konstantin Zyryanov as they threatened to rack up a more emphatic victory margin.
It was easily the most impressive Russian performance of Euro 2008 and if they reproduce this quality against the counter-attacking style of the Dutch in Basel on Saturday, it will be an exciting affair.
"This is a huge win for a side still under construction, with lots of young players and some experienced," Russia coach Guus Hiddink said.
"It gives me real pleasure to work with them. The youngsters have learnt lots.
"We're very proud of what the team have achieved in this tournament," he said. "But that's not enough.
"The next goal are the Dutch. Our problem is we only have two days to recuperate.
"I don't have 20 A-players. Holland used their B-team last night against Romania. Their A-team have had five or six days to recover."