The Newspoll survey for The Australian newspaper showed voters were divided roughly 50-50 in their support between Gillard's Labor party and Abbott's Liberal-National coalition, once voting preferences were distributed.
Around 44 per cent of voters put the opposition as their first choice against 38 per cent for Labor, with the remainder of votes allocated from smaller parties using a voter preference system.
The poll of 1,600 voters was carried out on Tuesday and Wednesday, after a Newspoll at the weekend put Labor ahead by four percentage points.
A Galaxy poll for the Herald Sun newspaper on Thursday gave Labor a 52 per cent lead to the opposition coalition's 48 per cent.
Undeterred, Abbott, who doubts the science behind climate change, is telling voters that Labor will introduce a carbon tax that will lead to higher power bills for everyone.
He is the Liberal party's third leader since it lost power, and the first to threaten the government in opinion polls.
Some polls have suggested that the election may result in a hung parliament, but most analysts expect her centre-left Labor party will hang on to power for a second three-year term with a slim majority.
Pollster Martin O'Shannessy, chief executive of Newspoll, predicted Labor would scrape through the election with a four or five seat majority in the 150-seat House of Representatives.
Labor gained power in 2007 with 83 seats after 11 years in opposition.
O'Shannessy said Rudd's popularity plummeted in Newspoll surveys since May after he shelved plans to make big polluters pay for the carbon gas they emit, and created Gillard's chance to strike.
"The big strategic weakness in the Labor campaign has been the failure to satisfactorily explain the change of leader"
Norman Abjorensen, political scientist, Australian National University
But Labor's rebound in the polls under Gillard proved short-lived after she announced in the first week of the election campaign that greenhouse gas polluters will not be charged during Labor's second term.
Reneging on the key promise of Labor's 2007 election campaign to make polluters pay had created "a leadership crisis", said O'Shannessy, adding that people are saying "this leadership isn't what we signed up for".
Gillard is facing a backlash at the ballot box over a range of voter gripes including lingering anger over her unprecedented party power grab and her policy direction on climate change.
Nick Economou, a political scientist at Monash University, told the Associated Press news agency that continuing media attention on Rudd's demise reminds voters of their anger that the leader they had chosen had been taken from them.
In late June Gillard, who was then Rudd's deputy, stunned Australians, including many within the government, when she launched a sudden challenge to the prime minister's leadership.
"The big strategic weakness in the Labor campaign has been the failure to satisfactorily explain the change of leader and I think that's certainly going to hurt Labor and Gillard in Queensland [Rudd's home state]," Norman Abjorensen, a political scientist at the Australian National University, told the Associated Press.