But Storm Hunter came up trumps with wins in the women's singles and deciding mixed doubles to earn Lleyton Hewitt's team a late-night 2-1 victory in their opening tie at Sydney's Ken Rosewall Arena.
De Minaur looked rusty as Ruud made light work of the world No.7 to win 6-3 6-3 after Hunter had stepped in earlier on Saturday as a late replacement for Maya Joint to put Australia on the front foot with a 6-2 7-6 (7-3) win over Malene Helgo.
The hosts then salvaged victory as Hunter joined forces with John-Patrick Smith for the deciding mixed doubles against Ulrikke Eikeri and Viktor Durasovic.
Hunter and Smith clinched a 4-6 6-1 (10-4) victory in an hour and 17 minutes, finishing nearly half-an-hour after midnight.
Australia - out to claim their first United Cup silverware - will return to action on Tuesday, with de Minaur looking to bounce back against Czechia.
De Minaur had looked subdued as Ruud claimed the opening three games in less than 12 minutes en route to winning his first set off the Australian.
Norway's world No.12 then lifted his serving game in the second set to finish off the match in an hour and 34 minutes on de Minaur's home court.
It is three-time grand slam finalist Ruud's first win over de Minaur in three ATP matches dating back to 2019.
"I had a little bit of a slow start, but I think Casper played a very good match from the beginning to the end," de Minaur said.
"I had some chances and break points, but he served really well throughout the whole match and yet didn't really give me too many chances or opportunities."
Doubles specialist Hunter made an "emotional" return to the Sydney court earlier on Saturday as a last-minute replacement for Australia's top-ranked woman Joint.
World No.32 Joint failed to recover in time from an illness, but Hewitt will hope the 19-year-old rising star - set to be seeded at Melbourne Park - will be fit to face two-time grand slam winner Barbora Krejcikova on Tuesday.
Hunter wrapped up the opening set in 35 minutes, before Norway's world No.533 Helgo wrested the momentum following a marathon game at 5-5, which produced 11 deuces.
The 31-year-old Queenslander won the second-set tiebreak on her serve after an hour and seven minutes.
"This is pretty emotional for me," Hunter said while holding back tears.
"It's been a pretty tough two years, rupturing my Achilles and fighting my way back through surgery and relearning everything.
"I never thought I'd be back on this court in a singles moment playing for Australia."
The 2023 year-end doubles world No.1, Hunter had suffered an Achilles tendon injury during Billie Jean King Cup training in April 2024.
The popular veteran has clawed her way back to be ranked world doubles No.33 since making her comeback in February last year, but has slipped from a career-high singles ranking of No.114 to No.426.
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