Stunning Australia comeback over Czechs seals Davis Cup semis spot
Last year's runners-up almost crashed out in the last eight but Alex de Minaur pulled Australia back from the brink by beating Jiri Lehecka 4-6, 7-6 (7/2), 7-5 in the second singles rubber.
The world number 12 levelled the tie after Tomas Machac defeated Jordan Thompson 6-4, 7-5 in the opening battle and forced a deciding rubber, won by Wimbledon 2022 doubles champions Matthew Ebden and Max Purcell.
They defeated the returning Lehecka and Adam Pavlasek 6-4, 7-5 on a rollercoaster night for the team with the second most Davis Cup wins in the competition's history, 28, behind only the United States.
Despite their rich history Australia have not won the competition since 2003 and looked set for elimination with Lehecka serving for the tie against De Minaur, who dug deep to find a new level to keep his country's dream alive.
"I just told myself to keep fighting, keep playing till the last point, you never know, sometimes you get your chances," said De Minaur.
"I got a little sniff, I was able to roll with it.
"I think my reputation kind of is quite strong when it comes to these types of situations, it kind of precedes me - maybe I won that match because of that today."
The only time the Czech Republic have beaten Australia in 10 clashes was in 1975, but the three-time champions came extremely close in Malaga.
"We were one game from going home, for him to fight back and win that match is one of the best comebacks I've ever seen," said Ebden.
Australia captain Lleyton Hewitt has been one of the most critical of the controversial updated Davis Cup format which began in 2019, and Green and Gold fans were outnumbered by Czech supporters at the Martin Carpena arena.
Over two-thirds of seats were filled, although the atmosphere could not match surprise package Finland's win over reigning champions Canada on Tuesday, willed to life by a few thousand noisy Nordic fans.
Machac, 23, slapped a forehand winner down-the-line to break Thompson in the first game and it was enough to secure him the first set.
The second was just as tight and when Machac broke for 5-4, Thompson immediately battled back to pull level, breaking the Czech for the first time in the match.
Machac broke again though with a passing shot and clinched the match with another forehand winner.
"I only got one break and it was an absolute battle to get it," said a disappointed Thompson.
His defeat left the pressure on De Minaur's shoulders to keep the Green and Gold in the hunt for their 200th tie victory.
Stunning comeback
Lehecka broke for a 3-2 lead in the first set and held off De Minaur in the epic final game, surviving five break points and eventually converting his fourth set point.
The Czech, ranked 31st in the world, broke again for a 2-1 lead in the second set, which he held on to, surviving three more break points for a 5-3 lead.
However Lehecka froze when serving for the tie, going long repeatedly and broken to love by a De Minaur who suddenly found another gear, winning 10 consecutive pointsand dominating the tie-break to force a decider.
De Minaur broke Lehecka to start the third set and consolidated it, but the Czech broke back for 2-2.
The Australian took a 6-5 lead when he broke again and wrapped up the set to love to complete his superb comeback.
"It's great to have such amazing support, this is an Australian Davis Cup team, we fight until the end and we're never dead," said De Minaur.
The consistent Ebden and Purcell pairing only dropped two points on their serves in the first set and broke in the seventh game to take it.
They pressed the Czech duo on their serves in the second set and eventually found a way through to move 6-5 ahead, serving it out to send Australia through to face Finland on Friday.
On Thursday Novak Djokovic's Serbia face Great Britain and Jannik Sinner's Italy play the Netherlands in the remaining last eight matches.