Thanasi Kokkinakis and Alex de Minaur have dragged Australia into the Davis Cup finals group stage via a thrilling 3-2 qualifying win over Hungary in Sydney.

The unfancied Hungarians had taken a shock 2-1 lead with a stunning doubles victory on Saturday, before de Minaur and Kokkinakis embarked on a steely rescue mission at Ken Rosewall Arena.

Kokkinakis sealed the tie for Australia with a 6-4, 6-4 triumph over Zsombor Piros.

De Minaur had earlier come out on top in the marquee match-up against Márton Fucsovics with an electrifying 7-6 (7-4), 6-4 victory.

The great escape marks only the third time this century the Australians have overturned a 2-1 deficit in Davis Cup.

Mate Valkusz and Fabian Marozsan's 6-4, 6-4 doubles defeat of John Peers and Davis Cup debutant Luke Saville had Australia staring down the barrel of an inglorious exit from the competition.

Hungarian captain Zoltan Nagy only drafted Valkusz -- ranked 1,312th in doubles and the world number 439 singles player -- in as a last-minute replacement for Fucsovics.

Fucsovics was rested after defeating Kokkinakis 7-6 (7-4), 1-6, 6-3 in Friday night's second singles rubber to level the tie at 1-1 after de Minaur gave Australia the early initiative with a 7-5, 6-2 victory over Piros.

But despite Hungary easing Fucsovics's workload, de Minaur wore the world number 35 down in the sapping humidity under the arena's closed roof on Saturday.

De Minaur rallied from 3-0 and 4-2 down in the crucial first-set tiebreaker and then withstood a fierce second-set fightback from Fucsovics to finally seal the must-win on his fourth match point.

"This Aussie team is going to do everything to leave it all out there on the court," de Minaur said.

"We've got immense pride, immense passion and one thing you can count on from the Aussie Davis Cup team is we're never going to give up."

The full make-up of the 16-team group stage, to be played at yet-to-be-determined European locations, will be decided after the completion of this weekend's other 11 qualifying ties.

AAP