Lleyton Hewitt's team, runners-up in the World Cup of men's tennis for the last two years, are now odds on to make the 'final-eight' week in Malaga in November after following up their 2-1 win over France with another victory over the injury and illness-hit Czechs on Thursday.
Thanasi Kokkinakis, again entrusted with the tricky No.2 singles spot by captain Hewitt, came up trumps once more on the indoor hard court once more, maturely dealing with the erratic firepower of rising teenage star Jakub Mensik in an impressive 6-2 6-7 (2-7) 6-3 victory first up.
Captain Lleyton Hewitt was rewarded for keeping faith in Kokkinakis. (Dan Himbrechts/AAP PHOTOS)
It followed Kokkinakis's victory over French ace Arthur Fils in the opening tie on Tuesday and justified Hewitt's decision to choose him ahead of the higher-ranked Jordan Thompson.
Then the Czech challenge crumbled after just eight minutes of the second rubber when their No.1 Tomas Machac, who had been forced to retire with cramp during his loss to Carlos Alcaraz in Wednesday's loss against hosts Spain, again pulled out, this time with injury, against Alexei Popyrin.
The battle between the two No.1s turned into a farce as it immediately became obvious that Machac, moving stiffly and with right calf heavily strapped, shouldn't have been playing at all as he needed courtside medical attention after losing just the first game.
At 15-30 down on his own serve in the second, Machac offered a resigned hand to Popyrin, gifting the Australians victory after just nine points, with just the doubles still to come.
The reason Machac was forced to play was because the Czechs, who had only four men in their team, had been hit by another matchday blow when their No.2 singles man Jiri Lehecka was forced out with illness.
The victory put Hewitt's team in a hugely powerful position to reach the eight-team finals week after a second group B victory, with a tie against the Alcaraz-inspired hosts still to come on Sunday.
There is still, though, the outside chance that France or Spain, who play on Friday, could also finish with a 2-1 winning record to pip them.