A stunning eleventh-hour bid to abolish a controversial electoral fairness clause in South Australia's constitution has won unexpected parliamentary support — and ignited fury in the state Liberal Party.

During last minute legislative debate during the final sitting week of parliament — ahead of the March election — Labor abandoned its push for a referendum on constitutional issues and instead voted with key crossbenchers to abolish the constitution's electoral "fairness provision".

The provision is employed in a redistribution of electoral boundaries after each election and is designed — in principle — to deliver the party which wins the majority of the two-party-preferred vote enough seats to win government.

It was introduced under a Labor government in 1991.

The removal of the constitutional clause will have no impact on voting at the March election but could significantly shape how future governments are formed in South Australia.

The Liberals have long argued that successive boundary redistributions have failed to properly take the provision into account.

They say the evidence for that is the fact they have comfortably won the popular vote in three of the last four elections without winning government.

But their fortunes were reversed in last year's redistribution which made four Labor-held seats notionally Liberal.

The seats are Colton, Elder, Mawson and Newland.

Labor unsuccessfully challenged the redistribution on the grounds it changed the head count in electorates, delivering greater voting power to Liberal voters in country seats, and less power to Labor voters in suburban electorates.

Labor and the Greens join forces

In October, the Government announced plans to push for a post-election referendum on the issue, it argued, to restore the "one vote, one value" principle.

The plans were met with fierce opposition from the Liberals and conservative crossbenchers, meaning it was doomed for failure.

But in a stunning turn in Legislative Council debate, the Government indicated it now had legal advice the fairness provision could be removed from the constitution without a referendum.

Labor MLCs voted in favour of Greens MLC Mark Parnell's move to do just that and to review the electoral fairness provisions of the Constitution after the election.

The move was supported by Independent John Darley, who had previously indicated his opposition to the Government's position.

Mr Darley's shift drew a furious response from Shadow Treasurer Rob Lucas, who accused Mr Darley of engaging in a "dirty deal" with Labor and the Greens to dud the Liberal Party.

"It has been dropped on the table and it has clearly been discussed with some other members of the chamber and our party has not seen it," Mr Lucas said.

"We are not aware of what the amendment does.

"A Labor Party inserted those fairness provisions, supported by Independents and the Liberal Party at the time in the constitution. They were supported by a referendum. My question is: if something has to be inserted by a referendum, how do you, without a referendum, actually remove them?"

SA Best Leader Nick Xenophon, whose party is expected to carry significant sway in the new parliament, has indicated he is in favour of a major overhaul of the constitution's electoral fairness provisions.