With over 99 per cent of ballots counted, voters in the electoral district centred on the town of Tapolca in west Hungary gave Jobbik's candidate Lajos Rig around 35.3 per cent, to 34.4 per cent for his Fidesz rival.
The official result may not be announced until Thursday after ballots from abroad are counted, Hungary's election office said yesterday.
The success is the latest landmark on Jobbik's rise after it achieved its highest ever share of the vote - around 20.5 per cent - at last year's parliamentary election.
As its success rises, Jobbik's leader Gabor Vona, 36, who once founded a paramilitary group that preyed on the Roma minority, is toning down the party's rhetoric which stigmatised Roma as criminals.
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Orban's right-wing Fidesz party and its junior coalition partners, the Christian Democrats, have ruled Hungary with an all-powerful two-thirds majority since 2010.
Fidesz has suffered a sharp drop in popularity since the end of last year however following corruption scandals and unpopular policies like an Internet tax that was later dropped after mass protests.
Last month an Ipsos poll showed Fidesz at 21 per cent and Jobbik at 18 per cent. Only around 200,000 people separated the two, in a country of 10 million.
"There is a mood to change the government in Hungary, and now there is the force to change it as well," Jobbik leader Gabor Vona said at a press conference yesterday.
Csaba Toth, an analyst with the Republikon Institute, told AFP Jobbik can now believe it will be the main challenger to Fidesz in the next general election, which is scheduled for 2018.