Podemos, which means "We Can" in Spanish, would garner 24.1 percent of the vote if elections were held today, according to the Sigma Dos poll for TV station Telecinco.
The party, with university professor Pablo Iglesias as its most public face, came just ahead of the main opposition the socialist PSOE, which had 23.7 percent support despite choosing a telegenic new leader in Pedro Sánchez in July.
It is the first time that a nationwide poll has put Podemos in second place ahead of the socialists.
The poll showed support reaching 28.3 percent for Prime Minister Mariano Rajoy's ruling conservative Popular Party, which swept to power in a landslide general election win in November 2011.
Podemos has plugged into discontent with big establishment parties, threatening an end to a two-party political system that has dominated Spain since its return to democracy following the death of longtime dictator Francisco Franco in 1975.
The party which raised cash through crowdfunding stormed past older opposition groups to take fourth place in Spain's EU elections in May, winning 8.0 percent of the vote and five seats in the European Parliament, despite having been officially formed just four months earlier.
It backs a guaranteed minimum wage, lowering the retirement age to 60, stopping hospital privatizations and eliminating tax havens.
Podemos has been accused of populism and of defending the policies favoured by late Venezuelan President Hugo Chavez.
But earlier this month the party approved a resolution on the economy that no longer talks about defaulting on part of Spain's public debt as it had advocated in its European election platform.
Party leaders now speak instead about an orderly debt restructuring process to return to more sustainable debt levels.
The shift was seen as part of an attempt to tone down some of its initial proposals in an effort to appeal to a wider centre-left constituency as the party aims to be a potential election winner.
Members of the Podemos grouping last week held a critical vote on the party's future structure and platforms, with the ballot closing on Sunday.
Results made public on Monday show that the faction led by Pablo Iglesias won 80.71 of a vote in which 112,070 people took part.
The victory for the proposals put forward by Iglesias' team will see the party headed up by a secretary general. The party structure will also include a management team and a citizen's council, as the party gears up for Spain's general elections, expected in late 2015. Voting for candidates to fill top roles will take place from November 10th to 14th.
The leadership team of Podemos has not yet decided if the party will stand in municipal elections in Spain in May 2015.
The Sigma Dos poll queried 800 people on October 16-20.