Duckworth squandered a big first-set lead before falling 7-6 (8-6) 6-4 to Safiullan, the world No.167, in Tuesday night's opening singles rubber in Sydney.
The deflating defeat leaves Australian No.1 Alex de Minaur needing to upset world No.2 and reigning US Open champion Daniil Medvedev in the second singles match to keep the tie alive.
Australia and Russia both hold 1-0 records in the competition following respective wins in their opening ties.
De Minaur inspired a surprise victory over Matteo Berrettini's Italy, while Safiullan was the unlikely hero in Russia's win over France after Medvedev was a shock three-set loser to Ugo Humbert.
The 2015 Australian Open junior champion, Safiullan rose to the occasion once again.
Despite trailing 5-2 in the opening set, he broke back to snatch the first set as Duckworth's first serve deserted him.
Coming off his best season yet in 2021, Duckworth was unable to reprise the tennis that has propelled the 29-year-old into the top 50 for the first time.
The world No.49 was broken again trying to stay in the match at 4-5 in the second set.
De Minaur must now orchestrate a huge boilover over Medvedev to force the tie into a decisive doubles encounter between Medvedev and Safiullan and Australia's nominated pairing of Luke Saville and John Peers.
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