Labor is expected to easily win Saturday's election but opinion polls show One Nation at 22 to 28 per cent, outpacing the Liberal vote at 14 to 20 per cent.
Premier Peter Malinauskas queued for almost an hour at a booth in his electorate of Croydon on Saturday morning, along with his wife Annabel and children, Jack, George, Eliza and Sophie.
Mr Malinauskas said he had followed his election day ritual of going for a run before heading to the Woodville Gardens booth with his family.
"It's the first time I've voted with four kids, which brings its own challenges," he said.
The premier's four young children waited patiently in the poll queue, but were understandably wilting by the time their parents finally arrived at the ballot box.
They were rewarded soon after with democracy sausages, with their father telling them "team Mali, dad's got to go and do some work" as he rushed off for an appearance with Prime Minister Anthony Albanese.
Liberal leader Ashton Hurn voted at Angaston Town Hall in her Barossa Valley electorate of Schubert before heading to Adelaide to visit other booths.
One Nation leader Cory Bernardi was among the record 454,862 (34.5 per cent) South Australians who cast their ballots at early voting centres, which opened a week ago.
Another 174,000 (13.2 per cent) had requested postal ballots, meaning almost half the 1.3 million eligible voters had potentially voted before election day.
In a final opinion poll released on Friday, YouGov forecast a 59-41 win for Labor on a two-party preferred basis against both the Liberals and One Nation - a 4.4 per cent swing in its favour.
YouGov's Paul Smith said Labor was set to secure its largest two-party preferred vote in SA history, while the Liberals were on track for 19 per cent, their worst result in any state or federal election since the coalition was formed.
"One Nation's surge to 22 per cent places them second in the state for the first time, with particularly strong support in regional areas," he said.
Adelaide University emeritus professor of politics Clem Macintyre said the rise and rise of One Nation had the potential to create a watershed moment in Australian politics, and the end of two-party politics at a federal level.
"If they do make a breakthrough, they're going to have to work hard to be a more serious and viable alternative government," he said.
"It's more frustration with the major parties … I think we can still say One Nation is a party of disaffected voters."
Flinders University public policy associate lecturer Josh Sunman said One Nation's discipline had been the surprise story of the campaign.
He said One Nation had delivered targeted messaging and candidate discipline, and "I was expecting a lot more candidate scandals and meltdowns".
Hours after he commented, a UK court issued an arrest warrant for One Nation's Aoi Baxter over a charge of sexually touching a woman without consent, and he was swiftly disendorsed.
The state's 600 polling booths are open from 8am to 6pm, when counting begins.
