Hurkacz was pushed all the way by the Australian lucky loser Kokkinakis before emerging with a 6-7 (10/12), 7-6 (9/7), 7-6 (8/6) victory.
At five hours and 45 minutes it was the Briton's longest match in a storied career characterised by comebacks both on and off the court
Andy Murray, who had already used all of his bathroom allocations, wasn't allowed to leave the court to relieve himself
In front of a raucous but weary Margaret Court Arena in Melbourne, the Briton finally prevailed 4-6, 6-7 (4/7), 7-6 (7/5), 6-3, 7-5
Australian Open doubles champion Thanasi Kokkinakis won a decisive singles rubber to power 28-time winners Australia through to the next stage of the Davis Cup Saturday where they were joined by fellow multiple champions Spain and France
Australian bad boys Nick Kyrgios and Thanasi Kokkinakis won the Australian Open men's doubles title on Saturday, beating compatriots Matthew Ebden and Max Purcell on Rod Laver Arena.
Tennis' bad boy Nick Kyrgios was at it again Thursday, smashing a racquet and flipping a finger at the crowd as he and partner Thanasi Kokkinakis ensured an all-Australian Melbourne Park men's doubles final for the first time in 42 years.
Nick Kyrgios claimed Saturday a coach and trainer associated with Croatian doubles opponents Mate Pavic and Nikola Mektic threatened to fight him after the top seeds were bundled out of the Australian Open.
Roger Federer will be replaced by Spain's Rafael Nadal when the rankings are released at the end of the tournament.
Thanasi Kokkinakis, who is nursing a shoulder injury that has kept him out of this year's Australian Open, dismissed the offers from match-fixers as little more than comments from "randoms" on social media.