It is therefore Germany who will travel to Madrid for the semi-finals on Saturday while Leon Smith’s side head home and must win a qualifying tie in early March to book their place in next year’s finals.
This tie was once again played behind closed doors but both teams provided vocal support, particularly during the doubles clash, which could scarcely have been tighter.
Kevin Krawietz and Tim Puetz were unbeaten having got the better of Novak Djokovic and Nikola Cacic in their group win over Serbia and they were marginally the better team in the opening set, forcing Skupski to save a set point at 5-6.
Salisbury and Skupski held a 6-4 lead in the tie-break but could not take any of their four set points and, with each point ratcheting up the tension, it was Germany who struck.
The second set followed a similar pattern but Britain looked set to force a decider when they led 5-0 in the tie-break only for Germany to win seven points in a row, sparking huge celebrations.
Germany captain Michael Kohlmann sprang a surprise by selecting Gojowczyk, who had not played a Davis Cup match since 2014 and was on a five-match losing streak, for their opening singles instead of Dominik Koepfer.
Having been expecting to face a left-hander, Evans instead found himself up against a right-hander, but Gojowczyk made a horribly nervous start and never recovered while his opponent got better and better as the Brit won 6-2 6-1.
Evans revealed afterwards he was unhappy with his morning warm-up but he rated his performance one of his best of the year.
The 31-year-old said: “I practised pretty poorly. I stayed out on the practice court a little longer. Just pressure, a pressure situation today. Got a bit angry. I think Leon hit the nail on the head, it’s sort of good to have a bit of an edge on days like today.
“It’s not his best match by any stretch, obviously, but I think I contributed a lot to that. I took on his second serve early. I made him hit the double faults. I’m not stupid. I know he hadn’t played Davis Cup for a little while and I used that to my advantage.”
Norrie has had an outstanding season and played the number one role with aplomb against France and the Czech Republic but, after turning his match against Struff around, he was outhit in the deciding set.
Norrie will rue the opener when, from 1-4 down, he clawed his way back and served for it at 6-5 before leading 6-4 in the tie-break.
He looked to have done to Struff what he has to so many opponents this season with his relentless hitting and attitude when he took the second but for once Norrie looked a little physically laboured and he lost the final five games to fall to a 7-6 (6) 3-6 6-2 defeat.
The 26-year-old, who has climbed from 71 in the rankings to 12 in 2021, certainly deserves a holiday but it is only a month until the new season begins with a very similar competition in the ATP Cup, where he will again lead the British team.
Additional reporting by PA Sport.