A poll by the Kantar TNS and Median agencies for the Czech Television showed on Sunday that 45.5 percent of Czechs would vote Zeman against 45 percent in favour of Drahos, with the rest undecided.
"This is a showdown between two completely different candidates representing two parts of a rather split society," Tomas Lebeda, a political analyst at Palacky University in the eastern Czech city of Olomouc, told AFP.
Zeman, an ex-communist known for his pro-Russian and pro-Chinese stance, topped a field of nine candidates in the first round on January 12-13 with 38.56 percent of the vote, ahead of Drahos with 26.60 percent.
Zeman's attitude to the European Union echoes other populist-minded eastern EU leaders -- especially in Hungary and Poland -- at odds with Brussels over mandatory refugee quotas and various rules which they see as attempts to limit national sovereignty.
The 73-year-old makes no secret of his staunchly anti-Muslim views, and once called the 2015 migrant crisis "an organised invasion" of Europe, claiming Muslims were "impossible to integrate".
Even though the country of 10.6 million people has only received 12 migrants under the EU quota system, migration has become a key issue in political campaigning.
"If you want to stop them (migrants), you have to stop them at the beginning, otherwise you can never stop them," Zeman said in a TV debate on Monday.
Since the first round, billboards all across the Czech Republic sought to appeal to voters with anti-migrant messages: "Stop immigrants and Drahos. This is our country. Vote Zeman!"
"Milos Zeman represents low-income groups with lower education, who more often live outside cities and typically in regions with lower economic performance, and of course he has adjusted his campaign to that," said Lebeda.
"He is a candidate with a long-term, systematic foreign-policy focus on Russia and China, and a candidate who is not really accepted by western politicians."
- 'I want to replace that man' -
Drahos, a 68-year-old former head of the Czech Academy of Sciences and a chemist by profession, could not be more different.
A mild-mannered liberal centrist whom critics have branded "wishy-washy", he has called for Prague to "play a more active role in the EU" and backed the adoption of the euro.
He is also a critic of the refugee quota system, but contends that the Czech Republic is strong enough to accept its allotted 2,600 refugees.
"Jiri Drahos has no political career behind him, but judging by his statements, he is a pro-Western politician whose priority is a focus on the European Union," Lebeda said.
In a rare display of emotion, Drahos exclaimed at a meeting with supporters on Monday: "I want to replace that man at the Prague Castle!"
Drahos will rely on backing from most of the failed first-round candidates.
Zeman, in turn, has the backing of embattled billionaire Prime Minister Andrej Babis.
- A second chance for Babis? -
Babis's populist ANO movement won October's general elections with its anti-corruption and anti-euro campaign, but the Slovak-born tycoon -- who is facing police charges over EU funding fraud -- has failed to woo coalition partners.
Tapped by Zeman for prime minister in December, Babis was forced to form a minority government which failed a confidence vote on January 16.
On January 19, parliament voted to strip Babis of immunity as a lawmaker, allowing the police to proceed with the charges.
Babis is due to submit his cabinet's resignation to Zeman on Wednesday.
But Zeman said he would give Babis a second try, in line with the constitution, before his presidential term of office expires on March 8.
"Regardless of the presidential election result, Mr Drahos will not have a chance to give or not give Mr Babis a second try," Zeman said.
Drahos said earlier he had a problem with a prime minister facing police charges.
More about: #Czech