Labor holds Batman by the slimmest of margins, but a concerted effort by the Greens could mean the party may lose the seat in today's by-election.
Mr Shorten told supporters "they wrote Labor off in Batman and you have proved them wrong".
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.
"We will be back."Greens candidate Alex Bhathal has run and lost in the seat of Batman six times".
Kearney posted Twitter shortly after, claiming that her win belonged to Batman and all those who backed her in a tight race.
"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.
Mr Shorten said Ms Kearney would be the first woman to hold the seat in 112 years.
"Many people have said over the course of the campaign that regardless of the outcome, we'll have a strong, progressive woman representing us in this seat".
Critically, Kearney's victory brings the proportion of women in the federal Labor caucus to 48% while the Liberal Party remains at 22 percent.
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"That didn't come off", Mr Butler told ABC radio. In the electorate during voting on Saturday, Shorten said Kearney "has done wonders to lift confidence in Labor in this electorate".
Party supporters chanted ecstatically "Ged! Ged! Ged!"
He told the Greens election night party at the Preston brewpub Tallboy and Moose that the result would either be known within a few hours, or not for several weeks.
Earlier, the Greens MP Adam Bandt, who worked alongside Bhathal throught the 34-day campaign, said a low voter turnout could have affected the vote.
It's unclear whether Bhathal, who was on her sixth attempt to win the seat, will stand again. The byelection was caused by Feeney's resignation in the citizenship crisis.
The Greens began the race as favourites after the minor party won a landslide victory in a state byelection previous year in the seat of Northcote, which roughly encompasses the southern end of Batman.
The Stop Adani campaign, which has been campaigning heavily in the progressive seat in an attempt to wedge Labor into withdrawing support for the Queensland coalmine, has raised concerns that a Labor win in Batman rewards the party for equivocating on the project.
But Ms Bhathal's candidacy was also dogged by the leak of a 101-page party complaint accusing her of bullying and intimidation, something she repeatedly denied.