Hardie, who stepped up as captain for the second four-day game against New Zealand A, smashed a splendid 115 at Bert Sutcliffe Oval in Lincoln in a timely knock.
The 24-year-old West Australian scored almost half of Australia A's total of 253 after they were sent in to bat on Saturday.
The Black Caps moved to 1-37 at stumps on day one, with South Australia quick Jordan Buckingham breaking through for a vital wicket before the close of play.
Hardie has been in the sights of chairman of selectors George Bailey and his panel for a couple of years, but this innings will seriously push his claims after another impressive season for WA.
After smashing an unbeaten 174 in the 2021-22 Sheffield Shield final, Hardie again proved himself as a big-game performer by taking four wickets and scoring a crucial 45 to help WA to back-to-back titles last month.
Opener Matt Renshaw, who played two Tests on Australia's recent tour of India, was unable to build on his century in the first game in New Zealand and was dismissed by Scott Kuggeleijn for two.
Renshaw batted in the middle order in India and against South Africa at the SCG in January, but slotting in at the top seems his most realistic way back into the Test side.
Veteran David Warner is under mounting pressure to save his red-ball career ahead of the World Test Championship against India and the Ashes.
Australia A had three ducks in their 69-over innings, as New Zealand capitalised on a bowler-friendly pitch.
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