Labor’s Ged Kearney has bucked the trend of shifting demographics in inner-city Melbourne, fighting off a tenacious Greens campaign to win the Batman byelection.

Ms Kearney was projected to win 53 per cent of the two-party preferred vote, to 47 per cent for Greens’ candidate Alex Bhathal, who was running in the seat for a sixth time.

“Our campaign spoke to everyone, from the [Western] Ring Road to the river,” Ms Kearney said, noting the demographic differences in the north and south of the electorate.

The former nurse and ACTU president thanked the union movement for its support, saying “I think there was a nurse on every booth today”.

“Guess what – I’m on my way to Canberra,” a delighted Ms Kearney told supporters in the inner-north suburb of Thornbury.

Her victory is a win for Opposition Leader Bill Shorten who announced a controversial tax policy on the eve of the byelection – and it defies predictions the Greens would cruise to victory in the increasingly gentrified electorate.

Mr Shorten told supporters “they wrote Labor off in Batman and you have proved them wrong”.

Labor was projected to claim a 2 per cent swing, and was likely to also win more primary votes than the Greens.

The Greens conceded defeat about 9.30pm.

Richard Di Natale blamed “hard-right” preferences for Labor’s win. Photo: AAP

In a gracious concession speech, Ms Bhathal noted voters had told her during the campaign that, regardless of the result, Batman would be represented by a “progressive woman” and that it was an “honour” to contest the seat against Ms Kearney.

“Obviously it’s not the result all of us would have wanted,” Ms Bhathal said.

Greens leader Richard Di Natale said Labor had benefited from preferences from “hard-right parties”.

The Greens began the race as favourites after the minor party won a landslide victory in a state byelection last year in the seat of Northcote, which roughly encompasses the southern end of Batman.

Labor had been expected to bleed more votes to the Greens south of  Bell Street, the electorate’s arterial road known colloquially known as “the hipster-proof fence” where gentrification has seen the area change rapidly.

But polling booth returns showed Ms Kearney managed to hold Labor’s support in the north of the electorate, and won a swing to Labor in the Greens’ southern strongholds of Northcote and Thornbury.

Earlier on Saturday, there were accusations of dirty tricks as some older voters reported receiving robo-calls telling they did not need to vote in this election.

The northern section of the electorate has a sizeable multicultural community, and some voters reported that the calls were in their own language.

It was not clear who was responsible for the calls, but Labor sent out last-minute text messages to Batman voters urging them to come to the polls.

The election-day controversy underlined the bitter tone of the campaign, a rare Labor-Greens contest, which has seen both parties attack each other over campaign tactics and the behaviour of party activists.

Ms Bhathal was also forced to deny allegations of bullying from Greens members from her local branch who leaked a 101-page dossier of complaints against her.

The byelection was triggered by the resignation of Labor MP David Feeney, who quit over dual citizenship.