Australia absorbed the injured Alex de Minaur's absence to beat France 2-1 in their group-stage opener in Spain on Tuesday (Wednesday AEST).
Thanasi Kokkinakis set Lleyton Hewitt's team on their way with a tight boilover win against Arthur Fils but Alexei Popyrin was blown away by an inspired Ugo Humbert.
That meant the Valencia battle came down to the doubles and Purcell and Matt Ebden delivered, beating Pierre-Hugues Herbert and Edouard Roger-Vasselin in three tense sets, 7-5 5-7 6-3.
With Spain and the Czech Republic to come it was a crucial result for an Australian team watched on the sidelines by Aussie No.1 de Minaur, whose hip injury prevented him featuring.
The top two from each group will progress to the quarter-final stage, in Malaga, from September 19.
Purcell said there were no nerves despite the high-stakes, high-quality battle to decide the tie.
"I backed the fact Matty and I do so well when we're positive," he said.
"Any team that comes in against us at 1-1 probably feels like they've lost the day anyway."
World No.86 Kokkinakis had got Australia off to the ideal start, defeating world No.24 Fils 7-6 (7-4) 7-6 (7-3).
The battling Kokkinakis came back from 4-2 down in the second set, saving a series of break points - a running backhand was particularly crucial - to force the tiebreak.
That — Davis Cup (@DavisCup) @TKokkinakis backhand on the run �#DavisCup | @TennisAustralia pic.twitter.com/IS1USkVEzCSeptember 10, 2024
"Thanasi did great ... he dug deep (in the second set) ... I thought he was capable and had a lot of confidence in him," Hewitt, in the last Australian team to win the Davis Cup in 2003, said.
"The boys had to come out in the live doubles and we have full belief. But it's never easy and it's not something we take for granted, how tough it is.
"But these guys came up clutch for us."
Kokkinakis said he stepped up his preparation when he saw, in New York, that de Minaur was still to fully recover from the hip injury he suffered at Wimbledon, realising he might start.
"I knew he wasn't 100 per cent and was struggling, so my focus changed. I was like, 'I need to be ready here. I need to have a little bit more purpose when I train'," he said.
"Lleyton trusted me to go in there and do the job and give my best effort and I'm very happy with the way it went."
With in-form Popyrin, the New York conqueror of Novak Djokovic next up, Australia seemed poised for a winning 2-0 lead.Â
But Popyrin ran into an inspired world No.17 Humbert, who blew the Australian away 6-3 6-2.Â
Alexei Popyrin's good form deserted him in Valencia, the Australian losing to Ugo Humbert. (EPA PHOTO)
That meant the doubles became the decisive rubber, with Purcell, champion with Jordan Thompson at Flushing Meadows, reprising his Wimbledon 2022 winning partnership with doubles veteran Ebden.
The match began badly for France with Herbert not only double-faulting his first-serve point but doing so by whacking the serve into his teammate. However, France managed to save a break point and hold, and the set went with serve to 6-5.
Three successive Ebden passes to break Roger-Vasselin won the Australians the first set and they held a match point in the second set on Herbert's serve.
It went the distance though, Australia gaining an early service break and Purcell defying some wobbles to win the tie.
Czech Republic begin their campaign against Spain on Wednesday before backing up to face Australia on Thursday.
Australia and Spain complete their group stage action on Sunday.
35°C