Labor secured its best result in South Australian election history with an increased majority of a least 32 seats in the 47-seat lower house and about 39 per cent of first-preference votes.
One Nation finished in the top two in around half of the seats, based on counting on Sunday afternoon, securing more votes statewide than a Liberal opposition that was only certain of holding four seats, with a handful of others in doubt.
The anti-immigration party's candidates were in the running in four seats, three previously held by Liberals, with as-yet unclear preference flows to determine the results.
Premier Peter Malinauskas said the outcome "obviously has a lot to unpack within it".
"I think one of those things is that in a world of serious volatility, we see that play itself out at the ballot box locally," he said.
Former ABC election analyst Antony Green described the poll as one of the most challenging he had worked on, with preference flows in "ultra-complex counts" often failing to reflect primary voting intentions.
Flinders University public policy lecturer Josh Sunman said the state would have to wait weeks for a full result in one of the most complicated elections the nation had seen.
"But these really complex, fragmented counts … are becoming the new normal," he told AAP.
One Nation leader Pauline Hanson pointed to state head Cory Bernardi's success in winning his upper-house seat, adding the party would be going hard at November's Victorian state election.
"There's a movement, there's an undercurrent and it's people saying we've had a gutful," she told Sky News.
"We want our country back. We want to have a voice."
While the 22 per cent primary vote is One Nation's best result in nearly 30 years at a state election, it must wait to learn if it has won any lower-house seats.
The party claimed a similar vote share in the 1998 Queensland election and won 11 seats in the then-89-person parliament, but it now holds no seats in its home state.
The huge significance of the Labor victory had been lost amid the focus on One Nation, Mr Sunman said.
"This is a massive victory, but a dampener for them is they didn't manage to make any regional inroads, which they'd been hoping to," he said.
"The really significant takeaway is that while One Nation didn't win a massive amount of seats, in the outer metro area in particular, it is now the second party - they are Labor's competitor, not the Liberal Party."
Speaking in the former Liberal stronghold of Unley, an inner-Adelaide seat that Labor hadn't held for 32 years, Mr Malinauskas said there was no such thing as a safe electorate.
"This seat now has a margin of over 10 per cent for Labor," he said as Bentleys, BMWs and Range Rovers whizzed past.
The premier met Governor Frances Adamson on Sunday morning with a clear view to "establishing a government sooner rather than later".
Across Adelaide, Labor won Colton, Morialta, Unley and Hartley from the Liberals.
But the party's leader, Ashton Hurn, was defiant and upbeat in her assessment while conceding the results were "really tough".
"There'll be a lot of lessons that we need to learn as a team so that we can make sure that we can drive forward into the future towards 2030," she said.
Ms Hurn added she would remain in the role that she took up in December to make sure her party presented a "really strong alternative" for SA voters.
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