His 6-2 3-6 6-1 defeat by world No.587 Taa Baadi on Monday (Tuesday AEDT) provided Morocco with their first ATP Tour match winner in eight years.
Vukic, 29, who reached a world ranking high of 48 in 2023, is currently ranked 84th and had a run to the quarter-finals of the Adelaide International in January.
The home crowd's delight was soon doubled when another Moroccan wildcard, world No.731 Karim Bennani, saw off France's Quentin Halys 6-4 6-7 (5-7) 6-2 in the next match on centre court.
"I don't know what to say. I still can't believe what just happened," Bennani, who at 18 became the youngest Moroccan to win an ATP match, said.
"Thank you to the amazing Moroccan crowd, my coaches, my parents ... I'm just really happy with the win."
Better news for another Aussie male in the United States.
Alex Bolt was a straight-sets winner over China's Wu Yibing at the clay court event in Houston.
After being pushed to three sets in his two qualifiers, the 33-year-old South Australian won 7-6 (8-6) 6-2 in 89 minutes and either American fourth seed Tommy Paul or Paraguay's Adolfo Daniel Vallejo await in the round of 16.
Bolt's compatriots Alexei Popyrin and Adam Walton begin their campaigns later in the week.
On the same surface in Charleston, Australia's fourth-ranked women's player Ajla Tomljanovic fell at the first hurdle.
Former world No.32 Tomljanovic, 29, was beaten 3-6 6-1 6-4 by Croatian Donna Vekic, who will next face fifth-seeded American Maddison Keys in the round of 32.
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