Igor Andreev kept Russia's hopes of retaining the Davis Cup alive by beating Chile's Nicolas Massu in the final rubber in La Serena.
Russia, underdogs in the tie at start of play, had seen their 2-0 lead evaporate after victories for Chile's doubles team on Saturday and then Fernando Gonzalez against Marat Safin, in straight sets, earlier on Sunday.
That forced the tie into a deciding rubber and Andreev delivered, denying the home crowd the result they craved.
Andreev took control early on and dropped only three games in the opening two sets.
Olympic champion Massu fought back by winning the third on a tie-break but Andreev's impressive serving - whe was not broken in the entire match - ensured he didn't wobble and went on to secure a 6-2 6-1 6-7 (1-7) 6-4 triumph.
Russia will now entertain France in April's quarter-finals after Richard Gasquet continued his fine form to seal their tie against Romania.
He beat Andrei Pavel 6-3 6-2 7-5 to give France a 3-1 lead. It was his second straight-sets win of the tie.
Andy Roddick conquered clay as the United States lived to fight another day.
The slow red surface has been something of a bane for American teams who had failed to win on clay for a decade in the World Group.
But 'A-Rod' outlasted Tomas Berdych to give the USA an unassailable 3-1 lead in their tie with the Czech Republic.
Roddick prevailed 4-6 6-3 6-2 7-6 (7/4) to seal the win for the USA.
The Americans will play host to Spain next.
Fernando Verdasco ensured the Spaniards' win over Switzerland with a rubber to spare when he beat Stephane Bohli 6-3 6-3 6-2.
Last year's runners-up Argentina are through also to the quarter-finals after beating Austria 4-1.
Teenager Juan Martin Del Potro claimed the winning point for last year's runners-up who had been depleted by the absence of David Nalbandian.
The youngster took advantage of his unexpected promotion by outlasting Jurgen Melzer 7-6 (7/4) 3-6 6-4 4-6 6-2.
In the dead fifth rubber, Guillermo Canas beat Alexander Peya 4-6 6-1 6-4.
Next up for Argentina is an away match with Sweden.
Robin Soderling had to dig deep for a tie-clinching rubber win over Max Mirnyi in Belarus.
In a four-hour epic, Soderling held on for a 6-7 (8/10) 7-5 6-7 (8/10) 7-6 (7/3) 6-3 win over his more experienced opponent, saving a match point in the process.
Sweden captain Mats Wilander hailed the prospect of playing at home next.
"I think we have a good chance against them (Argentina),'' said Wilander.
"[For the] last several years, our team played all of their Davis Cup matches away from home, and our spectators are looking forward to see us back home in Sweden.''
Tommy Haas' second win of the weekend gave Germany an insurmountable 3-1 lead over Croatia.
Croatia, winners of the Davis Cup in 2005, now face a promotion/relegation play-off later in the year.
But Germany have higher ambitions after Haas sealed victory with a 6-2 7-6 (9/7) 6-4 win over Ivan Ljubicic, who confirmed afterwards he would not play in Davis Cup again as it was taking "too much energy" out of him.
The Germans will next meet Belgium after Kristof Vliegen steered his country past Australia in a thrilling tie in Liege.
The Belgians had been pegged back from 2-0 up by a Lleyton Hewitt-inspired Australian side.
The former world number one took the tie to a deciding rubber with an epic 6-2 6-3 6-7 (4/7) 3-6 6-1 win over Olivier Rochus.
But Vliegen held his nerve to post a 6-4 6-4 6-4 win over Chris Guccione.