Partial official results, based on two-thirds of ballots being counted, gave her 43.6% of the vote.
Her nearest rival, former lawmaker Elisa Carrio, has admitted defeat with 22.6% of the vote.
If confirmed by the full count, Mrs Kirchner will succeed her husband Nestor Kirchner and become Argentina's first elected female president.
"We've won by a wide margin," she told supporters in a speech at her campaign headquarters at a hotel in Buenos Aires.
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"We have repositioned the country, fought poverty and unemployment, all these tragedies that have hit Argentines," she said, referring to the country's recovery from the 2001 economic crash.
Exit polls showed Ms Carrio, who ran on an anti-corruption platform, took one out of four votes nationwide and did well with middle and upper-class voters in urban areas.
Ex-Economy Minister Roberto Lavagna won 19% of the vote, partial results showed.
Mrs Kirchner needs more than 45% of the full vote, or 40% with a 10 point lead over the next nearest candidate, to win the presidency without facing a second round of voting.
The partial count gives her an apparently unbeatable lead, with double the votes of her rivals.
Mr Kirchner has governed for the past four years, but surprised the nation by deciding not to seek a fresh term.
Besides a new president, voters were choosing eight provincial governors, a third of the Senate and about half of the Chamber of Deputies.
Some 27 million people were eligible to vote.
Economy and crime
The economy and rising crime have been the two main issues in campaigning.
Mr Kirchner has overseen a return to stability and some prosperity since the economy collapsed six years ago, plunging thousands into poverty.
Mrs Kirchner's critics have attacked her for failing to outline exactly what her policies are, but voters said the opposition had failed to offer any real alternative.
Surprise candidate
Just a few months ago, Mr Kirchner was riding high in the opinion polls and looked set to continue for a second term.
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However, it was announced in July that his wife Cristina, senator for Buenos Aires province, would stand in his place. No explanation was given.
As candidate for the governing Front for Victory, she has promised to continue her husband's centre-left policies.
As well as facing comparisons with Eva Peron, Argentina's legendary former first lady, Mrs Kirchner has been compared to former US First Lady Hillary Clinton, who is also a lawyer and senator seeking to become the first elected female president of her country.
"I don't want to be compared with Hillary Clinton or with Evita Peron, or with anybody," she said recently.
"There's nothing better than being yourself."
1 comment:
Kirchner is a bad president that took us again 30 years back. The money he took from a province and put it abroad in his bank acocunt, has not returned yet after several years and claims made (over USd500 million). They threaten people to win. This is not democracy. And his wife is even worse than him.
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