Premier Peter Malinauskas vowed his party will "work our guts out for the next four years" after increasing its majority.
"Although this is the best result our party has ever achieved, it's very important that no one confuses tonight's result as adulation," he said.
As of Sunday morning, Labor is leading in 35 seats and the Liberals eight seats.
In a historic result, One Nation had a 19.2 per cent swing, while the Liberals vote collapsed with a 15.9 per cent swing against it, with nearly 40 per cent of the vote counted.
One Nation candidates were leading the primary vote in the lower house seats of Hammond, Mackillop and Ngadjuri, which would be decided on preferences.
One Nation Leader Pauline Hanson said it was unclear how many seats the party had won but pointed to SA leader Cory Bernardi's success in winning his upper house seat.
The party would be going hard for former federal Liberal leader Sussan Ley's seat of Farrer and at the Victorian state election, she said.
"There's a movement. There's an undercurrent, and it's people saying we've had a gutful. We want our country back. We want to have a voice," she told Sky News.
Mr Bernardi is smiling.
"Because today an earthquake has rattled the foundations of uni-party politics in South Australia," he said.
Liberal Leader Ashton Hurn retained her seat in the Barossa Valley and will remain in the leadership role.
Federal Liberal senator Anne Ruston said the party had been sent a clear message and needed to return to the centre right.
She said the party couldn't win by moving to the the right or the left.
At the Labor victory celebration, Mr Malinauskas read a Henry Lawson poem, The Duty of Australians, and noted that our patriotism was "less brash and boastful and more dogged and determined".
"Diversity has always been our greatest strength," he said.
A record 454,862 (34.5 per cent) people cast early votes and 174,000 (13.2 per cent) requested postal ballots, meaning almost half the 1.3 million eligible voters had potentially voted before election day.
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