Although Zeman was in pole position Saturday, the outspoken head of state was unlikely to win an outright majority, with a run-off expected on January 26-27.
Shouting the same slogan, the woman ran towards Zeman, who is running for a second term, in the polling station in the Czech capital, Prague, before being quickly wrestled to the ground by Zeman's bodyguards.
While the Czech Republic is the EU's richest post-communist member by economic output per capita - it also has the bloc's lowest unemployment and one of its fastest growth rates - Zeman has tapped into anti-migrant rhetoric resembling that of anti-establishment forces that scored gains in European elections past year.
While the president may influence efforts to break a government stalemate as the cabinet is likely to lose the first confidence vote next week, Czech financial assets have been largely immune to political uncertainty.
A recent poll for Czech Television showed the tide could turn in round two, with a possible win for Drahos with 48.5 percent of votes in the second round against 44 percent for Zeman.
Drahos could not be more different.
He has also lashed out against the EU's efforts to integrate refugees from the Middle East and Africa, once saying that Muslim migrants will impose Sharia Law, chop off thieves' hands and stone adulterous women in Europe.
With over 99 percent of ballots counted, Zeman led the pack of nine candidates with 38.65 percent of the votes, the Czech Statistical Office said on Saturday. Zeman was shocked and was took out of the room by two security guards. A mild-mannered liberal centrist whom critics have dubbed "wishy-washy", he has called for Prague to "play a more active role in the EU" and has backed the adoption of the euro. That message resonates with his supporters, even though virtually no Muslim migrants have tried to settle in the country of 10.6 million people. "It's clear that not everyone can agree, but the current president doesn't unite people, he divides them", Drahos added.
Prague voter Martin Sauta said he voted for Zeman as he has "the most consistent views", while his rivals are "completely shapeless".
Independent analyst Jiri Pehe said the vote highlighted a "polarized" society.
The remaining candidates with a chance to advance are not political newcomers: Mirek Topolanek, who served as prime minister from 2006 to 2009, and Pavel Fischer, a former diplomat.
Zeman says he is ready "to meet (Drahos') request" to face each other.
Under the Czech Constitution, the president picks the prime minister after a general election, one of the office's key responsibilities.
Babis's populist ANO movement won last October's general elections with its anti-corruption and anti-euro campaign, but the Slovak-born tycoon facing police charges over European Union funding fraud failed to woo coalition partners.
Babis said on Thursday he would vote for Zeman.
Zeman was elected in 2013 during the country's first direct presidential vote, a victory that returned the former left-leaning prime minister to power.
But the situation could change dramatically if Drahos wins. The polling stations will close at 22:00 on Friday night and the election will continue from 8:00 till 14:00 on Saturday.