Defending champion Brazil defeated Russia 25-19, 25-18, 27-29, 29-27 on Saturday and was looking for its fourth-straight World League volleyball title against France in yesterday's final.
Earlier, France beat Bulgaria 25-21, 25-20, 25-20 to reach its first-ever World League final.
Russia, which beat Brazil in 2002 for its only League title, trailed in the first two sets.
"We could not match the tempo Brazil offered us," Russia captain Konstantin Usahakov said.
Russia saved four matches points in the third set on Semen Poltavsky's spikes to stay in the match.
"In the first two sets we played at our best level but then Russia came strong," Brazil coach Bernardo Rezente said.
In the fourth set, Poltavsky, who scored 28 points for Russia, saved two more match points and Russia missed a chance to convert two set points before Brazil finally blocked back the winner.
"We are not at the level to beat Brazil right now," Russia coach Zoran Gajic said. "But it would be good if we learn from the match."
Gilberto Godoy scored 23 points for Brazil and Andre Nascimento had 23.
Brazil has won the title five times and never missed the League final stage since it was launched in 1990.
France lost to Serbia-Montenegro on Friday but advanced to its first semi-final on point difference.