The Russians, who won the 2007 tournament in Spain, beat 2009 runners-up Serbia 77-67 thanks to an excellent all-round display by forward Andrei Kirilenko, who finished the game with 14 points and 11 rebounds, France, aiming for their first title after they won the bronze medal in 2005, ground out a 64-56 win over Greece after allowing the 2005 winners to convert a mere 34 percent of their shots from the field.
Russia and France will meet in Friday's second semi-final after holders Spain, who won their first title in Poland 2009, take on surprise package Macedonia.
Injury-hit Serbia, who were missing point guards Milenko Tepic and Aleksandar Rasic, briefly looked capable of upsetting the Russians after scoring the opening four points of the game.
That was the last time they held the lead as Kirilenko and Timofey Mozgov began to dominate the boards and also carved out an avalanche of open shots for their team mates, who hit a total of seven three-pointers and scored a barrage of second-chance points.
Serbia's playmaker Milos Teodosic finished with a game-high 20 points, but he also committed nine turnovers which invariably resulted in fast breaks and easy points for the Russians.
The more athletic Russian team had nine rebounds and eight assists more than Serbia, who struggled to contain Utah Jazz forward Kirilenko at either end of the court.
Victor Khryapa and Andrey Vorontsevich added 11 points each while Aleksey Shved chipped in 10 to cap a balanced team effort for Russia.
"Hard and aggressive defence has always been the key to our success but today we also played well in offence and I am very happy that we were able to execute our game plan," Kirilenko told Germany's Sport 1 television.
"It will be a great game against the French who play aggressive offence and are led by one of the NBA's best point guards Tony Parker, so it will be a tough match-up but we should be fine if we stick to our defensive qualities."
The French trailed throughout the opening three quarters against Greece before their inspirational playmaker Parker took matters into his own hands and propelled the comeback with eight points in the final period.
Greece had made the brighter start and romped to a 15-4 lead early on, after grinding a usually lethal French offence to a halt with tight zonal marking.
With Parker struggling in the first three periods, Nando De Colo kept France afloat with good perimeter shooting while centre Joachim Noah held his own in the paint.
Watched by his father and 1983 French Open winner Yannick Noah from the terraces, the 26-year old Chicago Bulls centre nailed a crucial pair of free throws late in the game after he also made a vital steal at his end.
"My son played with a lot of passion and I am so happy the team have won this game for France, they are like a little family and they keep doing a great job in tight games," Yannick Noah said.
"These kids came here to qualify for the Olympics and they will surely also dream of making it to the final and clinching a podium finish."
Parker finished the game with 18 points and De Colo added 16 but their efforts might have fallen short of the target had it not been for a brilliant performance by Nicolas Batum, who scored 15 points with an excellent shooting ratio.
Earlier on Wednesday, hosts Lithuania, who suffered a shock 67-65 quarter-final defeat by Macedonia on Wednesday, beat Slovenia 80-77 in their 5th-8th place playoff match.
The result means Lithuania have secured a berth in next year's Olympic qualifying tournament while Slovenia, who host the next European Championship in 2013, were eliminated.
The winners and runners-up of Eurobasket 2011 will qualify automatically for the 2012 Games along with hosts Britain, while the next four teams in line enter an inter-continental 12-team playoff for another three berths.