Marat Safin was once again the Davis Cup hero for holders Russia as they pipped France 3-2 to take the last berth in the semi-finals.
Safin has only lost one of six deciding rubbers for Russia - that reverse came in 1998 on his debut - and last December closed out victory for his nation in the 2006 final against Argentina.
Safin always looked in control against Paul-Henri Mathieu as he sealed a 7-6 (7/3) 6-3 6-2 victory.
"I think it was surprising for me that I could play such good tennis," Safin told www.daviscup.com.
"I was injured for a couple of days, I couldn't practise because of the blisters, so it was pretty amazing. I was so confident, for some reason. I felt I was going to win, and with such confidence I felt there was no chance it would go five sets."
His team-mate Nikolay Davydenko said: "You never know with Marat.
"But he plays his best tennis in the Davis Cup and especially in Moscow."
Sebastien Grosjean's earlier victory over Igor Andreev in the first of the reverse singles had taken the tie to a deciding rubber.
The Frenchman prevailed 7-5 4-6 2-6 6-3 6-4 to take the tie to the decider, but his effort was to prove in vain as Mathieu suffered more cup heartache.
It was the third time that the 25-year-old had lost a fifth and deciding rubber against the Russians.
He was beaten from two sets up by Mikhail Youzhny in the 2002 and was thrashed by Igor Andreev in the 2005 quarter-final.
Victory hands Russia a home semi-final against Germany in September.
The Germans lost both of the dead rubbers to Belgium, having already wrapped up victory in Saturday's doubles.
Christophe Rochus beat Michael Kohlmann 3-6 6-4 6-4 before Dick Norman conquered Philipp Kohlschreiber 6-2 6-3 on Sunday.
The other semi sees Sweden play host to USA.
The Swedes, who also held a 3-0 lead going into Sunday's matches, shared the dead rubbers with Argentina to complete a 4-1 victory in Gothenburg.
Jonas Bjorkman beat Sebastian Prieto 6-1 6-2 before Juan Martin Del Potro restored some pride for the Latin Americans in the last rubber with a 7-6 (9/7) 6-4 victory over Robert Lindstedt.
The US shared their final-day rubbers with Spain to win through 4-1.
James Blake defeated Feliciano Lopez 6-3 7-6 (7-3) but Bob Bryan was beaten 6-4 6-4 by Tommy Robredo.
The US had already secured their place in the semi-finals when the doubles team of Bob and Mike Bryan beat the Spanish duo of Lopez and Fernando Verdasco 7-5 6-3 3-6 7-6 (7-5) on Saturday to give the Americans an insurmountable 3-0 lead in the series.
As a result Andy Roddick was rested on Sunday with Bob Bryan taking his place, but his defeat to Robredo was inconsequential.
"We won't have a hard time getting motivated and pumped up for the semi-final," American captain Patrick McEnroe said.
"The good news is it will be after a good summer of hardcourt tennis.
The guys usually play some of their best tennis that time of year.
Knock on wood, everybody's healthy, have good summers, and we can regroup for about a week, then get ready.
"I'm certainly not worried about losing momentum."