Their rise to third place in the polls comes despite a string of pre-election scandals.
One local candidate stood down after a picture emerged of her wearing a swastika armband.
Another was highlighted for posting racist and anti-immigrant comments online.
And yet, the revelations appear to have had little obvious effect on voters, even if the mainstream parties do not want anything to do with the party.
They are led by the dapper and clean-cut Jimmie Akesson, 35.
Voters also seemed unperturbed by the news that he has gambled half a million kronor (Â£43,000; 54,000 euros; $70,000) online.
"Every crisis the party gets into Mr Akesson handles very efficiently," says Ulf Bjereld, professor of political science at the University of Gothenburg, who sees him as a very skilful politician, if uncharismatic.
Any political party would struggle to fend off accusations of racism, he told the BBC, but the party leader simply took them off the list and said they were not welcome.
They will now occupy 49 seats in Sweden's 349-seat parliament.
By publicly stressing the Sweden Democrats' zero tolerance towards racism for the past two years, he has been careful not to fall out of step with the tolerance that Swedes believe they have towards ethnic minorities.
In contrast with other EU countries, Sweden is granting automatic residence to all refugees fleeing the Syrian conflict and some 80,000 people are expected to apply for asylum this year.
The Sweden Democrats have carefully refined their 2010 election platform, when their campaign commercial featured an elderly woman pushing slowly towards a welfare desk.
"You can choose if you want to save money from the pensions or immigration budgets," ran the commentary, over menacing music.
The pensioner is overtaken by a group of women in burqas.
The party made it into parliament in 2010 with 5.7% of the vote, five years after Jimmie Akesson took on the leadership.
Beforehand the party had been linked for years to neo-Nazis and other extremist groups.
In a speech in August, he identified himself as a nationalist but called for his party to show they were "broad and inclusive".
But he was forthright on the risks of political Islam.
"Islamism is the Nazism and communism of our time. It has to be met with disgust and much stronger resistance than has so far been the case."
The anti-immigration rhetoric has been toned down and carefully argued, with a policy of preferring to help refugees in their own countries.
There are obvious parallels with France's National Front which, under the leadership of Marine Le Pen, has moved into the political mainstream.
The two parties go back many years, and Ms Le Pen visited Jimmie Akesson last year in Stockholm. A few months ago he praised the National Front's "modern, quite fresh direction".
That does not mean the Sweden Democrats have shaken off their past but, with two MEPs in the European Parliament, they are now part of the same grouping as the Eurosceptic UK Independence Party - the Europe of Freedom and Direct Democracy group.
Swedish voters are attracted to the party, more because it gives a voice to people who dislike the political elite than its stance on immigration, Prof Bjereld believes.
And although he argues that party membership will always have a racist element, the main stance is more xenophobic than racist.
"One of Jimmie Akesson's skills is that he sends one message to the racists in his party and another to the general public."
They see themselves as the kingmakers of Swedish politics and, after polling 13% in national elections, the far-right Sweden Democrats are now difficult for mainstream parties to ignore.