The 68-year-old Drahoš - a physical chemist and former head of the Czech Academy of Sciences - set himself apart from the pack of challengers to Zeman with a strong, self-assured performance in the final televised debate, held late Thursday.
No candidate is expected to take the lion's share of votes today-polling puts Drahos between 22-27% and Zeman 34-42%.
The vote, likely to end in a run-off in two weeks, is seen as a referendum on 73-year-old Zeman, in office since 2013, who has harshly criticized migration from Muslim countries and is keen to boost ties with Russian Federation and China.
The woman, identified in a Femen statement as Angelina Dash, had the slogan, "Zeman, Putin's Slut" scrawled across her naked chest, a reference to Zeman's close relations with Russian President Vladimir Putin.
The two highest-scoring candidates will go head-to-head in a run-off planned for January 26-27.
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 previous year.
Drahos could not be more different. 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.
The student, who attends a secondary school in Prague, also said Mr Zeman's health problems were a concern. Former diplomat Pavel Fischer had 10.09 percent, entrepreneur Michal Horacek 9.09 percent and doctor Marek Hilser 8.80 percent.
Security personnel also had to help a visibly rattled Zeman, who walks with a cane, to leave the room.
"I congratulate Jiri Drahos for this attractive second place".
Trump wants immigration compromise - and border wall
But in the meeting he indicated a willingness to compromise with Democrats, whose votes are needed in the narrowly divided Senate. A former Trump appointee who resigned after a probe into a tribal loan program he oversaw is running for Congress in New Mexico.
Ibuprofen and Infertility in Men Linked by Study
The widely-used over-the-counter painkiller ibuprofen may pose a threat to male fertility , suggests a small new study . They tracked how ibruprofen affected them, noting that the painkiller can affect your body's hormone levels.
"Nvidia announces 65" 120Hz displays with 4k resolution, HDR and g-sync
While people are getting more and more interested in playing games on the big screen using a TV might not be the ideal solution. The screen will feature G-Sync so that there is no tearing and the experience is as immersive as it can get.
After casting his ballot in Prague, Lubos Seidl said the election boiled down to "a clash between the people who think the old way and those who think the new way".
Zeman's speech "was in sharp contradiction of our foreign policy and the president had no mandate to do it", Sobotka said at the time.
Many voters remained undecided until the last minute, with Prague archivist Marcela Riegerova saying she "ended up tossing a coin to decide between two candidates, and Drahos came out the victor".
Zeman had 40 percent, with 90 percent of the vote counted.
Independent analyst Jiri Pehe said the vote highlighted a "polarized" society.
Under the Czech Constitution, the president picks the prime minister after a general election, one of the office's key responsibilities.
Zeman was elected to the largely ceremonial post in 2013 during the country's first direct presidential vote, a victory that returned the former left-leaning prime minister to power.
A win by any of Zeman's main rivals could mean that voices from the Czech leadership may shift closer to the European Union mainstream.
But if one of the rivals wins, this will represent a huge change in the politics of this country that celebrates its 25th anniversary this year.
"Drahos has made it very clear that a prosecuted man should not be prime minister", Pehe said.