Foreign Minister Kurz propelled his party to the top of opinion polls when he became leader in May, dislodging the far-right FPO that had led for a year.
Austrian Foreign Minister and leader of the conservative Austrian People's Party (OeVP) Sebastian Kurz and his girlfriend Susanne Thier speak to media as they leave after casting their ballots in Austrian parliamentary elections on October 15. Kurz has taken a hard line, calling for limits on the number of refugees entering Europe and benefits cuts for European Union migrants living in Austria.
The 2015 influx of hundreds of thousands of people fleeing the war in Syria and poverty elsewhere into the EU's prosperous heartland left Austria with almost 100,000 new and mostly Muslim migrants.
Postal votes in Austria's parliamentary election will be counted on Monday to settle a close race for second place between the Social Democrats (SPO) and the far-right Freedom Party that will shape coalition talks with the young conservative victor.
Public broadcaster ORF's projections showed the SPO at 26.9 percent, while the FPO was projected to get 26 percent.
Immigration has dominated the campaign. Mr Kurz plans to cap benefits for refugees at well below the general level and bar other foreigners from receiving such payments until they have lived in the country for five years.
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Unlike Germany's far-right AfD party - which won its first seats in the Bundestag in the federal elections there last month - the FPO has a long history in Austria's Parliament and was part of a coalition government between 2000 and 2005.
Austria was governed by a coalition led by Chancellor Kern's SPO and Kurz's OVP, but that partnership collapsed in May, prompting a snap vote.
Experts say a right-wing government could turn Austria into a tricky partner for the EU.
'The Freedom Party as a government partner will not make a good impression in Europe (and) Kurz is aware of that, ' commented Der Standard newspaper in its weekend edition.
Although the Social Democrats have come either first or second in elections since World War II, voters are now more receptive to calls for tougher migration rules than the party's focus on social justice.