Great Britain are through to the Davis Cup quarter-finals after Joe Salisbury and Neal Skupski showed their quality to win a decisive doubles rubber against the Czech Republic.
Knowing Britain would be out if they lost, Salisbury and Skupski won 6-4 6-2 against Czech pair Jiri Vesely and Tomas Machac in Innsbruck, Austria.
It completed the fightback with Cameron Norrie winning after Dan Evans lost.
Leon Smith’s team will now play Germany in the last eight on Tuesday.
Germany, who are without ATP Finals champion Alexander Zverev, finished top of Group F after beating Austria later on Sunday.
Britain’s place in the last eight was hanging in the balance going into the doubles match, with Evans having lost to an inspired Machac before Norrie dug out victory over Jiri Lehecka.
Those results left two-time Grand Slam men’s doubles champion Salisbury and the vastly experienced Skupski, both ranked inside the world’s top 20, needing victory to clinch top spot in Group C.
“Today was tough. You look at the rankings and people think it is straightforward but it is never like that in the Davis Cup,” said British captain Smith.
“I’m thrilled for these guys [Salisbury and Skupski]. To come out and play as well as they did speaks volumes. We asked for passion, determination and the quality comes after that. I’m really proud of them.”
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If Salisbury and Skupski had lost and Britain were beaten 2-1 in the three-match group tie, it would have not been enough to qualify as one of two best-placed runners-up.
They would have finished second in the group because the Czech Republic would have had a higher percentage of sets won at the 18-nation finals.
Salisbury and Skupski, who won an ATP title together in San Jose last month, were overwhelming favourites, but had lost their doubles rubber against France on Saturday.
Once the pair clinched the first set on Sunday, they continued to grow in confidence and played with cohesion on the way to wrapping up a commanding victory.
Skupski served out the win, with Vesely knocking a return wide on match point, as the British team – making all the noise in a quiet arena which was without fans because of coronavirus restrictions in Austria – celebrated jubilantly.
A tight first set swung the way of the British duo when two double faults from Vesely contributed to a break for 5-4 and Salisbury served out.
The second set saw Salisbury and Skupski tightening their grip, breaking in the first game before moving 4-1 ahead and wrapping up victory with few problems.
“We wanted to start with a lot of energy and positively and play free. It definitely worked in the end,” said Skupski.
Salisbury, who won his first Davis Cup point after making his debut this year, said the moment felt “very special”.
“It was an amazing atmosphere even though we don’t have fans here. Our support team are making it feel like a great atmosphere even with nobody else here,” added the world number three.
“Playing for your country and getting the win is special.”
Norrie levels after Evans’ defeat gives Britain work to do
Britain’s campaign at the Davis Cup Finals – which sees group ties held in Innsbruck, Turin and Madrid before the semi-finals and final take place in the Spanish capital – was given the perfect platform by a victory for Evans in Saturday’s opening group tie against France.
But the world number 25 could not replicate that performance against Machac, who was making his Davis Cup debut this week.
The expression of Evans, one of bemusement and shock, showed his concern after a first set where he was overwhelmed by the athletic Machac’s stunningly high level.
After Evans’ frustration boiled over in the first game of the second set with a racquet smash, he began to improve.
The level of the British number two continued to move upwards until he served for the set at 5-3, spraying two forehands wide and hitting another into the net to gift the break back.
All that momentum which Evans had regained was quickly lost as Machac took control, winning the final five games to seal the biggest success, by ranking, of his career.
That meant Norrie needed to win for Britain – without the resting Andy Murray – to stand any chance of topping the group.
Norrie, ranked 12th in the world after a stunning season, looked likely to earn a straight-set win as he raced through the first in 29 minutes.
Hitting at his relentless best, Norrie made just two unforced errors as he broke Lehecka’s serve three times.
There was a complete contrast in the second set, however. as Norrie surprisingly started to misfire and it allowed Lehecka to move 5-1 in front before calmly serving out to level.
But the 26-year-old Briton regained control in the decider, using his experience and belief from a wonderful year to seal victory.
‘Britain pleased everyone has contributed’ – analysis
Russell Fuller, BBC tennis correspondent in Innsbruck
Great Britain did not dominate either of these ties, but they thoroughly deserved to go through.
Leon Smith sides very rarely fail to reach the quarter-finals and the captain will be especially pleased everyone has contributed.
Cameron Norrie has a 100% record; Dan Evans got the team off to a flying start against France’s Adrian Mannarino on Saturday; and Joe Salisbury and Neal Skupski were very sharp when Britain’s future in the Finals was on the line.
The players love their hotel in the mountains and they are used to the speed of these courts, so they will be more than happy to stay in Innsbruck for a quarter-final.
But they will definitely be on the move on Wednesday. Either back to the UK or to Madrid for a Saturday semi-final.
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