Australia's ruling coalition won a strong victory at a crucial special election yesterday that was heralded as a "renaissance" for the embattled Prime Minister, Mr Malcolm Turnbull.

Following a vicious campaign, the Liberal MP, Mr John Alexander, won a by-election in Sydney to ensure that the Liberal-National Coalition held onto its one-seat majority in Parliament.

The victory will help bolster the leadership of Mr Turnbull, who has come under heavy pressure due to the coalition's poor standing in the national opinion polls.

With about 73 per cent of the vote counted last night, Mr Alexander was expected to have suffered a swing against him of about 5.6 per cent but was due to defeat Labor candidate Kristina Keneally, by 54 to 46 per cent. Ruling parties in Australia typically suffer a swing against them at by-elections.

Celebrating his victory last night, Mr Alexander, a former tennis star, turned to Mr Turnbull and said: "This is a renaissance of your leadership. This event over the last five weeks, I think, under Malcolm, has brought us together," he said.

"It's been the most unifying and humbling experience."

Mr Turnbull, appearing elated, declared: "John Alexander, you are Bennelong's champion just as you were Australia's champion. John Alexander, winning another title."

The by-election, in the seat of Bennelong, was held after Mr Alexander was forced to resign because he realised that he was a dual citizen via his British father.

Australia has experienced an ongoing crisis in recent months which has forced nine MPs out of Parliament after it emerged they were in breach of a ban on political candidates holding a foreign citizenship.

The contest for Bennelong, in north-west Sydney, turned into a bitter fight, not least because the outcome was set to determine Mr Turnbull's future.

Much of the focus of the campaign was on efforts to secure the area's Chinese-Australian vote.

Bennelong has the highest proportion of Chinese-Australian residents of any electorate in Australia. About 21 per cent have Chinese ancestry, compared with 14 per cent with Australian ancestry.

Labor accused Mr Turnbull of being "China-phobic" after the government introduced laws to curb foreign interference which appeared to be aimed at Beijing.

But the mud did not appear to stick. A Liberal supporter, Mr Peter Qian, said yesterday that many Chinese-Australian residents voted on local issues rather than on the foreign interference debate and heightened tensions between Canberra and Beijing.

"There is a difference between what the Chinese newspapers (which were critical of the interference laws) report and what the people actually think," Mr Qian told AAP. "Most of them don't view the anti-foreign interference laws as necessarily targeting them."

But the swing against the Liberal party yesterday was enough for the Labor Opposition party to claim that its campaign was a success.

Labor was quick to point out that such a swing, if it applied nationally at the next election, due by 2019, would deliver it a strong victory.

The opposition leader, Mr Bill Shorten, said Labor had "a most remarkable wind in its sails" and paid tribute to Ms Keneally, a former state Premier of New South Wales.

"I salute a most remarkable candidate who has secured Labor a most remarkable swing," he said.

But it is Mr Turnbull who will end the year with the wind in his sails. He secured the legalisation of same-sex marriage and introduced the foreign interference laws, which have had strong public support.

Meanwhile, Labor suffered a blow when one of its MPs, Mr Sam Dastyari, was forced to resign on Tuesday following revelations that he adopted pro-China stances on Hong Kong and the South China Sea after accepting political donations from a wealthy property developer with links to China's Communist Party.

Labor has yet to replace Mr Dastyari and is rumoured to be considering turning to Ms Keneally, who ran a strong campaign in Bennelong.