The world No.9 found top gear on Sunday at Pat Rafter Arena, beating Kamil Majchrzak 6-3 6-3 to clinch a 3-1 result that sends Australia into the Cup's penultimate round next year.
With his backhand and serve firing, de Minaur followed up his 57-minute annihilation of Maks Kasnikowski on Saturday with another therapeutic response to a disappointing second-round US Open exit earlier this month.
Earlier, Max Purcell's scintillating tiebreak tennis alongside rock-solid Rinky Hijikata swung their doubles match - and the tie - in Australia's favour.
The pair's 7-6 (7-3) 6-3 defeat of Jan Zielinski and Karol Drzewiecki followed the win and the loss posted in singles by de Minaur and James Duckworth respectively on Saturday.
Purcell, on the comeback from a controversial 18-month anti-doping ban, turned the match on its head after a tight first set progressed to an inevitable tiebreak.
He drilled a backhand return to win the opening point on the Polish serve, then produced a pair of aces to shoot the hosts clear 3-0.
An unforced error from Poland was followed by two more Purcell winners, and he then held his nerve on a series of low volleys to eventually clinch the set.
Hijikata then held impressively and, after missing two break-point chances, nailed a forehand return to nab the match's only service break.
That was all Australia needed, with the composed pair energising the sold-out Pat Rafter Arena to secure a pressure-relieving victory in 77 minutes.
Australia's win followed a shock loss on the road to Ecuador earlier this year that plunged them into the must-win encounter against Poland.
They still need to win next year's qualifying round, against an opponent still to be decided, to progress to the finals in Italy in November, 2027.
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