Grabar-Kitarovic, a 46-year-old ex-foreign minister and former NATO official, had 51.4 per cent of the vote, according to exit polls released by the state-run HRT television.
Her rival, centre-left incumbent Ivo Josipovic garnered 48.6 per cent of the vote, said the exit polls released by the Ipsos Puls agency.
The first partial official results were to be released by the electoral commission on Sunday evening.
If they confirm the exit polls, Grabar-Kitarovic, the candidate of the main opposition HDZ party, will become Croatia's first woman president.
She would also become the first female head of state chosen by voters in the largely patriarchal Balkans region since Albania's Jatifete Jahjaga was elected by parliament in 2011.
The election for the largely ceremonial post was held as the European Union's newest member is grappling with a deep economic crisis.
Both Josipovic and Grabar-Kitarovic pledged to help kick-start the country's ailing economy.
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