Marat Safin came to the rescue for Davis Cup holders Russia by winning the decisive fifth rubber against France's Paul-Henri Mathieu in Moscow on Sunday.
Safin is now the fourth-highest ranked of the Russian players
Former world number one Safin has slipped down the rankings due to injury and loss of form, and played no part in the opening two days of the tie.
But after Sebastien Grosjean had beaten Igor Andreev, Safin saw off Mathieu 7-6 (7-3) 6-3 6-2 to give Russia a 3-2 win.
Russia will host Germany in the last four, and the US will travel to Sweden.
Grosjean kept the tie alive on Sunday with a superb 7-5 4-6 2-6 6-3 6-4 win over Andreev, leaving the stage set for Safin and Mathieu.
DAVIS CUP QUARTER-FINALS
Russia 3-2 France
Belgium 2-3 Germany
USA 4-1 Spain
Sweden 4-1 Argentina
Safin had missed the first two days with a foot injury, although he was far from certain to start as he is ranked below both Nikolay Davydenko and Mikhail Youzhny.
But Russia captain Shamil Tarpischev was confident enough to call on the former US and Australian Open champion for the fifth rubber and Safin came through, winning a tight first set before breaking early in the second and third.
"I didn't expect our skipper would put me on court this weekend and of course I never expected it would be so easy as I could not find my form in two recent months," said Safin.
"I had no doubts that I would win, and confidence is everything in tennis."
France captain Guy Forget said: "Good for them, they are the best team in the world. They can win again this year and despite everything we weren't far off."
On the final day in Gothenburg, Joans Bjorkman defeated Sebastian Prieto 6-1 6-2 before Juan-Martin del Potro beat Robert Lindstedt 7-6 (9-7) 6-4 to leave Sweden 4-1 winners over Argentina.
Belgium gave their home fans in Ostend something to cheer with two wins but the damage had already been done and Germany still came through 3-2.
Christophe Rochus beat Michael Kohlmann 3-6 6-4 6-4, and Dick Norman defeated Philipp Kohlschreiber 6-2 6-3.
The USA completed a 4-1 win over Spain in North Carolina after Bob Bryan went down 6-4 6-4 to Tommy Robredo, and James Blake beat Feliciano Lopez 6-3 7-6 (7-3).