Kubler scored a spirited 6-3 4-6 6-3 win over the higher-ranked Albert Ramos-Vinolas on Tuesday night to lock the Sydney tie up two rubbers apiece.
Kubler's victory, four nights after an equally rousing win over Britain's Dan Evans, gives playing co-captain Samantha Stosur and Tokyo Olympics mixed bronze medallist John Peers the chance to seal Australia's historic first United Cup tie.
Stosur and Peers will play Jessica Bouzas Maneiro and David Vega Hernandez in the deciding rubber at Ken Rosewall Arena.
Emerging star Olivia Gadecki earlier made an inauspicious United Cup debut, losing 6-2 6-2 to the 193rd-ranked Bouzas Maneiro to leave Australia trailing 2-1.
The dead-rubber tie was locked at one match apiece after Alex de Minaur upset Rafael Nadal on Monday night, before Maddison Inglis lost to Nuria Parrizas Diaz to level proceedings.
A late call-up to replace the injured Zoe Hives, Gadecki was making her first appearance in the green and gold since a Billie Jean King Cup doubles debut in November 2021.
The former teenage prodigy was headed for stardom before controversially sitting out the last Australian summer - including the 2022 Australian Open - after declining to be vaccinated against COVID-19.
Formerly coached by David Taylor, the esteemed ex-mentor of Samantha Stosur, Alicia Molik, Martina Hingis and Naomi Osaka, Gadecki made a swift rise up the rankings to a career-high No.156 in July last year.
Ash Barty has also taken Gadecki under her wing and will be courtside for her AO main-draw debut at Melbourne Park, after the 20-year-old was handed a wildcard entry from Tennis Australia.
While Gadecki has fallen out of the women's top 200, Kubler is set to soar to a new career-high ranking of around 80th next Monday following his two wins in Sydney.
The 29-year-old's new standing is nothing less than he deserves, after he was Australia's last player standing at the French Open and then reached the round of 16 at Wimbledon in July.
But he was cruelly denied a swag of rankings points after the ATP opted against awarding them at Wimbledon in protest at the All England Club's ban on Russian and Belarusian players because of Vladimir Putin's war on Ukraine.
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