She’s now scored a spot in Sunday morning’s grand-final, along with entrants from Greece, Belarus, Serbia, Cyprus, Estonia, the Czech Republic, Iceland, San Marino and Slovenia.
Miller-Heidke’s operatic rendition of Zero Gravity, a song about her experience of postnatal depression, saw her flying through the air atop a pole, flanked by two backing vocalists, and wearing a billowing white and pink gown.
Australia joined the Eurovision Song Contest in 2015 and has scored consistently well each year but never won.
The closest we came to the top spot was with Dami Im as our contestant in 2016. The former X-Factor star came in second with her song Sound of Silence.
Guy Sebastian represented Australia in 2015 and came fifth with Tonight Again, and Isaiah Firebrace performed Don’t Come Easy in 2017.
Last year, Jessica Mauboy came in 20th with We Got Love.
Since rehearsals began in Tel Aviv last week, Miller-Heidke’s performance has been the subject of increasing interest.
Following Miller-Heidke’s performance, Iceland’s entry made a shocking semi-final debut as they performed in leather and latex against a backdrop of pyrotechnics.
Techno-punk group Hatari attracted much attention in the lead-up to this year’s contest on Tel Aviv, Israel, with their darkly energetic track Hatrio Mun Sigra (Hatred Will Prevail).
They received the night’s loudest cheer, combining dance music, heavy rock and pop in front of an international audience at the Expo Tel Aviv. Iceland have participated in Eurovision 31 times since its debut in 1986, missing two years and finishing twice second but never earning the top spot.
Earlier, Netta Barzilai, last year’s winner, kicked off the event in her home nation with a rousing rendition of Toy, her Me Too anthem featuring bizarre chicken noises.
Seventeen international acts took to the stage on Tuesday night for the first of the semi finals and 10 made it to the grand final. The second semi final is aired on Friday, May 17 where another 10 finalists will be voted through, and they will all join the Big Five — Spain, UK, France, Italy, Germany and hosts Israel — to compete for the title.
The 10 finalists going through to the Grand Final of the Eurovision Song Contest on Saturday are:
🇨🇿 Czech Republic
🇸🇲 San Marino
🇸🇮 Slovenia#DareToDream #Eurovision pic.twitter.com/8YTnn4M6jH
Cyprus’ Tamta, Montenegro’s D Mol and Hungary’s Joci Papai were also among the first acts to perform.
The UK, as one of the “big five” countries, along with France, Germany, Italy and Spain, are already assured of a place in the grand final.
Last year’s winners Israel also do not have to qualify via the semi-finals.
The semi-final performances, including Kate Miller-Heidke’s, will be aired again tonight on SBS at 8.30pm.
Sunday’s grand final will air live at 5am and then again at 8.30pm on SBS.