Igor Andreev and Nikolay Davydenko fought off a stern challenge from French duo Sebastien Grosjean and Michael Llodra to put Russia 2-1 ahead after the doubles.
Davydenko was making his Davis Cup doubles debut and it took a while for him and Andreev to gel but after losing the first set, they combined well to take the next two. The French fought back to take the fourth set before the Russian pair secured the vital break in the fifth set to emerge 36 75 63 36 63 winners after three hours 23 minutes.
Russia is now just one match away from reaching the semifinals for the third year in a row while France has it all to do. The winner of the tie will be at home to Germany, who defeated Belgium with a day to spare, in September's semifinals.