The Russians celebrated their first Davis Cup title since 2006
World number two Daniil Medvedev celebrated the "best weeks" of his career as he led the Russian Tennis Federation to a third Davis Cup title.
Medvedev's 7-6 (9-7) 6-2 win over Marin Cilic sealed a 2-0 victory over 2018 champions Croatia in the Madrid final.
Andrey Rublev had won the first singles match against Borna Gojo 6-4 7-6 (7-5).
"It feels amazing but I am more happy for the team than for myself," said 25-year-old Medvedev, who did not drop a set at the Finals.
"It is never easy to come at the end of the season but it was the best two weeks of my career."
The Davis Cup triumph comes at the end of a season in which Medvedev won his maiden Grand Slam title at the US Open.
The Russians are the fourth nation to win both the Davis Cup and Billie Jean King Cup – the women's equivalent team competition – in the same year.
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Medvedev was initially tested in the first set by 2014 US Open champion Cilic, who had lost three of his four matches coming into the final.
The 33-year-old Croat built up a 4-2 lead in the first-set tie-break, but his forehand lost its way in the closing stages as the Russian steadied his own nerves.
Cilic's serve deserted him in the early part of the second set, with Medvedev going an early break up and keeping that advantage.
Andrey Rublev is the fifth most successful Russian in singles Davis Cup wins with 12
Russians dominate tennis team events in 2021
Rublev, 24, admitted he had felt the pressure when he started his team's campaign in Sunday's final.
But it did not show as the world number five lost just two points on his serve in the first set against Gojo, 22, ranked 274 places below him.
The second set was more competitive and Rublev's early tie-break lead was narrowed before he closed out a 6-4 7-6 (7-5) victory.
"It was super tough and I felt a lot of pressure but it's good to put my country in the lead," he told reporters.
The Russians, playing under the name of their federation because the nation is banned from international competition for doping violations, claimed their first title since 2006.
They were the pre-tournament favourites and have demonstrated why with some strong performances since the start of the year.
Medvedev, Rublev and Aslan Karatsev are in the world's top 20, while former world number eight Karen Khachanov is in the top 30.
Rublev and Medvedev were pivotal members of the team, with Rublev winning four out of his five matches, losing only to Spain's Feliciano Lopez in the group stage.
Their success as a team started with them winning the second edition of the ATP Cup at the start of the year.
Karatsev, who was on doubles duty over this week, then had a dream run through Australian Open qualifying to the semi-finals in February, losing to eventual champion Novak Djokovic.
There was a mixed doubles gold for Rublev at the Tokyo Olympics, all to the sound of Tchaikovsky's Piano Concerto No. 1 instead of the national anthem while the international competition ban continues.
'Crowd seemed happy' this time – Medvedev
However, the winning moment in Madrid was a muted celebration with a slightly less combative on-court interview after Medvedev previously baited the home crowd when he reminded the home crowd on Saturday that his team had eliminated Spain in the group stage.
"I didn't mean to offend with my celebrations, trying to emulate [Portugal's] Cristiano Ronaldo," said Medvedev, referring to the way he gestured to the crowd for calm after his team's semi-final win over Germany.
"I probably gave the wrong impression – it was not a good decision.
"But in the final it was amazing because there were a lot of Croatians in the crowd and the rest of the stadium was rooting for me. So the crowd seemed happy with our win and it looks like a good end of the story."
The tournament will return next year with more proposals to tweak the format to include a fourth group-stage city and a neutral host for the final stages, with venues yet to be decided.
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