One other exit poll broadcast after polls closed at 19:00 GMT also gave Geoana a lead.
Millions of Romanians voted in the decisive round of the elections that began at 7am (05:00 GMT).
A total of 12 candidates entered the race for the country's top position.
In the first round on November 22, Basescu captured 32.4 per cent of the vote while Geoana secured 31.2 per cent.
Basescu is endorsed by the ruling Democratic-Liberal Party (PDL) while Geoana is supported by the Social Democratic Party-Conservative Party Alliance (PSD), as well as the National Liberal Party and the Hungarian Democratic Union of Romania.
"Reason won't get to vote on Sunday. Most of the choices will be emotional ones. People will say either 'I can't stand Basescu any more' or 'I can't bring myself to vote for Geoana'"
Cristian Tudor Popescu, columnist for the Gandul newspaper
Both men claim they have the solutions to lift Romania out of a recession, form a government, eradicate corruption and restore public trust.
But neither candate has given figures on their economic plan for the country,
Romania's budget deficit is set to hit 7.3 per cent of GDP by the end of 2009.
The International Monetary Fund (IMF), the EU and the World Bank agreed in March to provide a $30bn loan to the country to help ease its economic crisis.
But the two lenders withheld payments in November following the collapse of the ruling coalition comprising Basescu's PDL and Geoana's PSD.
An interim administration has ruled Romania since the coalition fell apart, meaning that the winner on Sunday's poll will have to appoint a new prime minister.
While some analysts fear more futile political squabbling if Basescu wins, others say that Geoana will not be able to control certain PSD members suspected of corruption.
The election campaign has been marked by below-the-belt blows from both sides: Basescu notably came under fire from opponents after the release of a video apparently showing him slap a 10-year-old boy, footage he said was faked.
Cristian Tudor Popescu, a columnist for the Gandul daily newspaper, said: "Reason won't get to vote on Sunday.
"Most of the choices will be emotional ones. People will say either 'I can't stand Basescu any more' or 'I can't bring myself to vote for Geoana'
"Many Romanians are in despair that they can't vote with any conviction for either candidate. They feel like all they can do is try to stop the worse of the pair."