Exit polls from Austria's state broadcaster showed Mr Hofer, the far-Right Freedom Party (FPO) candidate who comfortably won last month's first round vote, on just 50.2 per cent.
The result will be a disappointment for Mr Hofer, a 45-year-old aviation engineer who is threatening to become the first far-Right head of state in the history of the EU, a result that could send political shockwaves through Europe.
His tally was less than half a per cent ahead of his opponent Alexander Van der Bellen, a 72-year-old retired political science professor and Green Party politician who ran as an independent.
Mr Van der bellen scored only 22 per cent in the first round, comfortably behind Mr Hofer's 35 per cent, but looks to have taken advantage of tactical voting among establishment and liberal Austrians determined to stop a far-Right presidency.
Election analysts said the final outcome would be decided in the cities of Vienna and Salzburg which are likely to favour Mr Van der Bellen over Mr Hofer, whose anti-immigrant, anti-austerity platform appeals Austria's small towns and villages.
"It will come down to Vienna. If Van der Bellen polls more than 60 per cent in Vienna he will win, if not - it's Hofer," Peter Hajek, a prominent Vienna-based pollster, told The Telegraph in Vienna. In official counting, as polls closed at 5pm local time, 75 per cent of votes had been counted, showing 52.6 per cent for Hofer and 47.4 for Van der Bellen.
The exit polls contained 'projections' for uncounted votes in the cities and among 700,000 postal votes, but analysts warned there was significant room for error in those numbers.
Senior European officials, including Martin Schulz, the socialist president of the European Parliament, have issued warnings that “Europe’s character will be changed” if the Freedom Party wins the largely ceremonial office.
While on the populist right, other leaders, like Marine Le Pen of France’s National Front and Geert Wilders, of the Dutch Party for Freedom, have hailed Mr Hofer's performance as the beginning a new “patriotic” anti-establishment revolution across Europe.
In an interview with The Telegraph last weekend, Mr Wilders said that a Freedom Party victory would open the door to re-shaping the European political landscape on populist lines.
“Just like a Brexit, a Freedom Party victory would be an enormous incentive for people all over Europe to see that we are not parties on the fringe of politics, that we could deliver not only the biggest party in respective countries but even provide the head of state, the elected President.
“It’s a reality and you’d better face it and deal with it. This will be the future in many European countries,” he said.
Mr Hofer has carried his Glock pistol around with him on the campaign trail, arguing that a rise in gun ownership in Austria is a natural reaction to the migrant crisis.
As voting got underway on Sunday, the contest was too close to call between Norbert Hofer of the right-wing Eurosceptic Freedom Party and Greens Party politician Alexander Van der Bellen, who is running as an independent.
Both men drew clear lines between themselves and their rival as they went into Sunday's race.
At his final rally Friday, Van der Bellen said he was for "an open, Europe-friendly, Europe-conscious Austria."
Asked as he arrived to vote Sunday what differentiated him from Hofer, Van der Bellen said: "I think I'm pro-European and there are some doubts as far as Mr. Hofer is concerned."
Hofer, in turn, used his last pre-election gathering to deliver a message with anti-Muslim overtones.
"To those in Austria who go to war for the Islamic State or rape women - I say to those people: 'This is not your home,'" he told a cheering crowd.
Later, Hofer sought to soothe international fears that he is a radical far-righter.
The Austria Press Agency cited him as telling foreign reporters Sunday that he is "really OK," and "not a dangerous person."
Austria’s Freedom Party was briefly sanctioned by the European Union when it last entered a coalition government in 2000, and has softened its public face since the days when it was fronted by Jorg Haider, who was widely accused of harbouring Nazi sympathies.
In 2000 some 150,000 Austrians took to the streets of Vienna to protest against the Freedom Party entering into Austria’s governing coalition, but protests have been much more muted during the 2016 campaing.
Only around 400 protestors were reported to have turned up to an anti-Hofer protest in front of Vienna’s Hofburg presidential Palace last Friday, carrying placards demanding “No Nazi in the Hofburg”.
The success of the Hofer candidacy reflects deepening discontent in Austria over immigration, unemployment and frustration over the iron grip that Austria’s two main parties, the Social Democrats (SPO) and the Austrian People’s Party (OVP) have retained since 1945.
“The Freedom Party has become the outlet for people who want to say ‘we’re fed up with this cosy consensus”, said Ian Bond, director of foreign policy at the Centre for European Reform, a pro-EU think-tank.
That sentiment was side reflected on the streets of Vienna this week.
"What I want is change," a florist near the famous Prater ferris wheel who gave his name only as Hans, says. "The only candidate offering change is Hofer."
Hans is an immigrant who came to Austria 30 years ago from the former Yugoslavia. But he says the influx of migrants has become too much. "The problem is criminality," he says. "Most of the refugees are fine, but 20 per cent of them are no good."
In April, a 21-year-old student was raped by three Afghan asylum-seekers in a public lavatory close to his florist shop at the Praterstern metro station. "You should see it round here at night," he says. "It's frightening."
Mr Hofer's anti-migrant rhetoric is winning support in unlikely places. Aydin Moradi, who runs a clothes stall in one of Vienna's street markets, came to Austria as a refugee from Iran seven years ago. But he says if he had a vote he would cast it for Mr Hofer.
"Most of the others round here wouldn't agree with me, but Hofer would be better, he'd sort it out," he says. "I'm not talking about real refugees, but half the people coming in now aren't refugees at all, they just come for the money and send it back home."
"Hofer is the only one who can bring change in Austria," Alfred Berger, a 53-year-old street cleaner, says. "I am for Hofer because of the refugee policy."
But others say a vote for Mr Hofer is dangerous, because it would allow the far-Right back into power.
"I'm afraid of Hofer," Edit Benkö, a psychologist, said at a protest against the Freedom Party candidate. "I'm afraid he will endanger the demoractic system in Austria."
Younger protestors were carrying banners denouncing Mr Hofer as a "Nazi", but Ms Benkö said she wouldn't go that far. "I don't think he's a Nazi, but he was a member of a far-Right fraternity," she says.
"I agree with Mr van der Bellen about the refugees," she says. "I'm not saying Austria should take them all and deal with the problem alone. It's a problem for all of Europe and we need a European solution. But it doesn't make sense to lock them out."
The migrant crisis has had such a major impact on Austria in part because it already has a huge immigrant population following a wave of Balkan migration in the 1990s.
Immigrants now account for around over a fifth of Austria’s population of 8.6m, with a further 90,000 remaining in Austria following last year’s immigration crisis that led to the closing of Austria’s southern borders.
"One thing worth noting is that in Vienna already more than half of all school beginners are from an immigrant background," said Dr Werner Fasslabend, president of the Austrian Insitute for European and Security Policy (AIES)
"In some schools it's as high as 80 per cent. As you can imagine, this is good ground for populists to build on."
("The Daily Telegraph", 22.5. 2016)
Additional reporting by Balazs Csekö
Foto: Leonhard Foeger/Reuters