The first goal came in the 23rd minute after a swift move by Russia, a pass by Yuri Zhirkov and the hulking presence of Pavel Pogrebnyak culminating in Finnish defender Petri Pasanen prodding the ball into his own net.
Russia, cheered on by a full stadium, continued to create chances, but as is so often the case with Guus Hiddink's young side, failed to take them.
In the 65th minute, however, the Finns decided to lend a helping hand, Veli Lampi turning a Konstantin Zyrianov pass into his own goal.
Andrei Arshavin added the third with just two minutes on the clock, sprinting through the Finnish defense to lift the ball over Jussi Jaaskelainen.
The result puts Russia into joint second place in Group 4 with six points from three games. Group leaders Germany face Wales, who also have six points, in Monchengladbach later on Wednesday.
Russia's next World Cup qualifier is not until March, when they host Azerbaijan.
There are nine groups in the European qualifying zone for the 2010 World Cup. Each group winner earns an automatic place at the finals in South Africa, while the best eight second-placed teams will play off against each other for the remaining four spots.
GROUP 4 (after 3 games)
Germany - 7
Russia - 6
Wales - 6
Finland - 4
Azerbaijan - 1
Liechtenstein - 1
