The new figures put the Pirates at 13 percent of the vote, pulling ahead of the Greens' 11 percent.
The survey, conducted by polling firm Forsa for the RTL broadcaster and Stern magazine suggested the struggling Free Democratic Party (FDP) could pull itself over the five percent hurdle needed to enter Parliament.
It has failed to do so in recent regional elections and other national polls have shown support of around two percent.
The poll suggests the current ruling coalition could continue, as Chancellor Angela Merkel's Christian Democratic Union (CDU) got 34 percent and its Bavarian sister party the Christian Social Union (CSU), two percent. This would give the current coalition parties a joint score of 41 percent.
The Social Democratic Party (SPD) managed a 24 percent showing, leaving its preferred coalition option of partnership with the Greens trailing at 35 percent.
The Left party posted an eight percent share.
The Pirates unexpectedly got 7.4 percent of the vote in the Saarland state election on March 25, and are expecting to clear the five percent parliamentary entry hurdle in the important North Rhine-Westphalia election in May.
“I'm hoping for 6.5 percent,” the vice chairman of the party, Bernd Schlömer, told the WAZ media group, referring to the May 13 vote.
But he appeared nonchalant about potential failure, adding “it's not tragic” if the pirates do not make it into the state parliament in that region – or in Schleswig Holstein, where voters go to the polls on May 6.
Meanwhile the party is showing signs that it is affected by internal strife just like any other political group.
A number of party members complained that the party was sexist and racist in an open letter published on Sunday evening in Die Welt Online.
The letter said a woman was described as being “too pretty” to be taken seriously. Another noted that in a Twitter discussion participants were told that it is okay to be “critical of foreigners.”
Aleks Lessmann, a spokesperson, said Monday that every party had a certain percentage of idiots, but it was important that such opinions were not shared by the majority.
“In contrast to the established parties we offer every basic member an equal forum.” Due to this openness, such discriminatory opinions “are more recognizable,” he said.
Lessmann said the people who run the national Pirate Party did not want to control what individual party members said. But he added, “The Pirate Party of Germany is clearly and unequivocally for equal rights, integration and a cultural getting along.”