"What would you like to say to your mum and sister?" the interviewer asked.
"F**k yeah!" McKeown exclaimed excitedly, before laughing and realising what she had said.
McKeown’s triumph came against a backdrop of family tragedy - her dad, Sholto, died in August last year.
Had Tokyo's Games not been postponed a year because of the coronavirus pandemic, he would have watched his daughter swim at an Olympics.
“I hope you’re proud and I keep doing you proud,” McKeown said.
McKeown entered Tuesday's final as world record holder but third-fastest qualifier behind American Regan Smith and Canada's Kylie Masse.
The Australian trailed her feted rivals at the last turn before a stunning surge in the final 30 metres delivered victory.
McKeown triumphed in 57.47 seconds, with Masse (57.72) taking silver and Smith (58.05) the bronze.
Australian veteran Emily Seebohm, at her fourth Olympics, finished fifth in 58.45.
McKeown will again meet Smith over 200m, with the Australian dropping the 200m individual medley from her program to focus on backstroke.
Her triumph comes against a backdrop of family tragedy, with her father losing his battle against brain cancer last August.
The swimmer dedicated her world record at Australia's selection trials to her father.
"I use it every day that I wake up," McKeown said at the June trials.
"I know it's a privilege to be on this earth and walk and talk."
With additional reporting by SBS News.