Victory over France on Saturday put Leon Smith’s side in a strong position in Group C but the three rubber format now played in the finals event leaves little room for error.
Dan Evans’ 6-2 7-5 defeat by Tomas Machac therefore put the pressure on his team-mates but they were able to deliver, with Cameron Norrie defeating Jiri Lehecka 6-1 2-6 6-1 before Joe Salisbury and Neal Skupski won the deciding doubles 6-4 6-2 against Machac and Jiri Vesely.
The victory means Britain stay in the quiet of locked-down Innsbruck for a quarter-final on Tuesday, which is likely to be a repeat of the 2019 clash with Germany, where Smith’s side came out on top.
When Smith first guided Britain to the last eight in 2014, it marked their best performance in 28 years, but this success means they have now at least replicated that in six of the last seven editions, capped by their title run six years ago.
The captain said: “I’m really, really proud of them. Doesn’t matter who wins or loses rubbers, everyone is in it together, everyone is supporting at the end.
“I thought Machac, who played Evo in the first match, played out of his skin. Then Cam plays another young guy who played out of his skin. Cam is so great at finding a way through.
“Then he starts playing some great tennis. That’s a testament because of who he is now as a player, the level he plays at. I’m really, really lucky to have him in the team.
“Then you get the doubles guys, who had a bit of a rough day yesterday. We had faith in them. They go about their business brilliantly. They prepared again. You always want to have a team of leaders. They stepped up. I thought they delivered just such a great performance.”
Machac is ranked more then 100 places below Evans but is on the rise and showed what a danger he could be by beating France’s Richard Gasquet on Thursday.
The 21-year-old played a sublime first set but, after smashing his racket and dropping serve in the opening game of the second, Evans worked his way back into the match and led 5-2. He played a horror game serving for the set at 5-3, though, and Machac reeled off five games in a row to clinch the biggest victory of his career.
“It was a difficult match,” said a disappointed Evans. “He played well. I didn’t play so well. (I) got myself in a winning position in the second set and didn’t take it. (I was) a bit indecisive really.”