The centre-right People's Party (OeVP), rebranded by Kurz, 31, as his personal turquoise "movement", is forecast to come first with over 30 percent, polls suggest.
But in a fresh triumph for Europe's populists just after Alternative for Germany (AfD) became the third-biggest party in parliament there, the Freedom Party (FPOe) looks set to be second or third with at least 25 percent - double the AfD's score.
Austria has had almost 150,000 asylum claims since 2015, making the wealthy Alpine country of 8.75 million one of Europe's highest recipients per capita.
Like the AfD, France's National Front and Geert Wilders in the Netherlands, the FPOe - which almost won the presidency in December - has stoked concerns about the influx, while also moving left on social issues.
"No, Islam is not part of Austria," party head Heinz-Christian Strache, 48, recently told a cheering, flag-waving FPOe rally.
Immigration must stop "until further notice", its programme says, and asylum is temporary.
"Strache is the counterweight to (German Chancellor) Angela Merkel whose 'welcome culture' is destroying Europe," one FPOe supporter told AFP, not wishing to give his name. "Austrians should come first."
"Wunderwuzzi" ("whizz-kid") Kurz took over the OeVP in May and ended its acrimonious "grand coalition" with the Social Democrats (SPOe).
Presenting himself as a breath of fresh air despite being in the government since 2011 and the OeVP having been in power nonstop since 1987, the foreign minister helped his party leapfrog the FPOe to lead opinion polls.
This was partly thanks to Kurz swinging to the right, talking tough on immigration and pledging to both shut Islamic kindergartens and cut welfare payments for foreigners.
Kurz and Strache also see eye-to-eye on lowering taxes, reforming Austria's bloated bureaucracy and wanting the EU to be less involved in how the country is run.
The once-mighty SPOe, in government for a total of around 60 years since 1945, looks set to be the main loser on Sunday despite it too taking a harder line on migrants.
Chancellor Christian Kern, 51, whose business acumen gave the SPOe hope when he took over last May, has suffered a string of mishaps, scandals and resignations.
Most damagingly, an Israeli election consultant - since fired - allegedly set up fake Facebook accounts with anti-Semitic content on behalf of the SPOe to damage Kurz.
Kern has said the SPOe will go into opposition if it doesn't win the election, making another "grand coalition" unlikely - unless a party coup topples him or he changes his mind.
The reaction abroad will likely be more muted than in 2000 when the FPOe under the late Jörg Haider, who called Hitler's employment policies "orderly", entered government and turned Vienna into a pariah.
But Austria could become a tricky EU partner.
Vienna will hold the bloc's presidency in the second half of 2018, just when Brussels wants to conclude Britain's talks to leave the bloc in March 2019.
Strache wants Austria possibly to join the Visegrad group of eastern and central European countries including Hungary and Poland, a thorn in Brussels' side.
He thinks Britain "will probably be better off after Brexit" and demands EU sanctions on Russia be lifted.
But Kurz too, and his ideas on everything from immigration to economic policy, could prove a source of conflict, said Patrick Moreau, an Austria specialist at the French National Centre for Scientific Research.
The young leader does not subscribe to the agenda of French europhile President Emmanuel Macron, who has outlined an ambitious reform proposal for the bloc, he said.
"Kurz's positions are pretty much diametrically opposed to those of French President Emmanuel Macron and are to a large extent in conflict with Merkel," Moreau told AFP.
“It's an explosive combination."