Great Britain will play in November's Davis Cup Finals as Henry Patten and Neal Skuspki won their doubles match to give the nation an unassailable 3-0 lead in their qualifying tie against Ecuador.
Toby Samuel and Arthur Fery both triumphed in their singles matches at a sold-out Copper Box Arena in London on Saturday to get Britain off to a winning start in the best-of-five tie.
Patten and Skupski then took to the court on Sunday and booked Britain's ticket to the 'Final 8' event in Bologna at the earliest opportunity with a 6-3 6-4 win over Gonzalo Escobar and Diego Hidalgo.
It is the first time that Great Britain have reached the knockout stage of the competition since 2023.
"Three years - it feels like quite a long time," Britain's captain Leon Smith told BBC Sport.
"To do it in three straight rubbers is really good and I'm actually delighted for the guys to look forward to something at the end of the year."
Even against underdogs Ecuador, whose singles players were both ranked outside of the world's top 200, there were doubts if Smith could lead Britain back to the knockout stages given his inexperienced team in London.
Jack Draper ended his difficult season early, while Jan Choinski and Jacob Fearnley were both unavailable through injury.
Smith was then dealt a late blow when British number two Cameron Norrie pulled out on Friday after feeling pain in his arm during a practice session.
However, Samuel - after a breakthrough season that has seen him rise from outside the world's top 250 to 95th in the rankings - stepped up on his Davis Cup debut.
Just weeks after winning his first Grand Slam match at the US Open, the 24-year-old overcame nerves and fought back from a set down to beat Andres Andrade 4-6 6-4 6-1.
Fery, meanwhile, was making just his second Davis Cup appearance as the British number one claimed an assured 7-5 6-0 win over Alvaro Guillen Meza.
And with world number one Patten and new US Open champion Skupski to call upon for Sunday's doubles rubber, victory seemed to be well within Britain's grasp.
The pair, despite not playing together on the ATP Tour, combined effortlessly and did not face a single break point against the Ecuadorians.
"We are good friends off the court, which I think always helps, and we spend time with each other when we are on the tour anyway," Patten told BBC Sport.
"[LTA coach] Louis Cayer has created the British system so it's quite easy for Brits to play together - we both have a good idea of what the other player is going to do, where they are going to hit it, where they are going to move to."
The last time Britain made it to the quarter-finals in 2023, they fell to a 2-0 defeat by Novak Djokovic's Serbia, with Norrie and Draper both losing their singles matches.
"When you get to the Final 8 and you play one of the seeded teams, they are extremely strong," Smith said.
"[Italy's Jannik] Sinner could be back playing, [Spain's Carlos] Alcaraz has talked about his commitment to it at the end of the year, but you've got a chance. You try and steal one of the singles, and it goes to the doubles and you've got a good doubles team.
"There's a lot of excitement about it, it brings the team together again."

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