The poll said incumbent President Petro Poroshenko was in a distant second place, closely followed by former Prime Minister Yulia Tymoshenko.
The election was shadowed by allegations of widespread vote buying. Police said they had received more than 1,600 complaints of violations on voting day alone in addition to hundreds of earlier voting fraud claims, including bribery attempts and removing ballots from polling places.
Volodymyr Zelenskiy, who stars in a TV sitcom about a teacher who becomes president after a video of him denouncing corruption goes viral, led the field of 39 candidates with 30.4 percent of the vote, according to an exit poll by the Kiev International Institute of Sociology and the Razumkov public opinion organization. Poroshenko tallied with 17.8 percent support and Tymoshenko had 14.2 percent, it said. The poll claimed a margin of error of 2.5 percentage points.
The top two candidates will face off in presidential runoff on April 21. Final results in Sunday's first round are expected to be announced Monday morning.
"Zelenskiy has shown us on the screen what a real president should be like," said voter Tatiana Zinchenko, 30, who cast her ballot for the comedian. "He showed what the state leader should aspire for — fight corruption by deeds, not words, help the poor, control the oligarchs."
Campaign issues in the country of 42 million included Ukraine's endemic corruption, its struggling economy and a seemingly intractable conflict with Russia-backed separatists in eastern Ukraine that has killed 13,000 people since 2014.
Concern about the election's legitimacy have spiked in recent days after Ukraine's interior minister said his department was "showered" with hundreds of claims that supporters of Poroshenko and Tymoshenko had offered money in exchange for votes.
Like the popular character he plays, Zelenskiy, 41, made corruption a focus of his candidacy. He proposed a lifetime ban on holding public office for anyone convicted of graft. He also called for direct negotiations with Russia on ending the conflict in eastern Ukraine.
"A new life, a normal life is starting," Zelenskiy said after casting his ballot in Kiev. "A life without corruption, without bribes."
His lack of political experience helped his popularity with voters amid broad disillusionment with the country's political elite.
"(We have) no trust in old politicians. They were at the helm and the situation in the country has only gotten worse — corruption runs amok and the war is continuing," said businessman Valery Ostrozhsky, 66, another Zelenskiy voter.
Poroshenko, 53, a confectionary tycoon when he was elected five years ago, pushed successfully for the Ukrainian Orthodox Church to be recognized as self-standing rather than a branch of the Russian church.
However, he saw approval of his governing sink amid Ukraine's economic woes and a sharp plunge in living standards. Poroshenko campaigned on promises to defeat the rebels in the east and to wrest back control of Crimea, which Russia annexed in 2014 in a move that has drawn sanctions against Russia from the U.S. and the European Union.
Speaking at a polling station Sunday, the president echoed his campaign promises of taking Ukraine into the EU and NATO. He said holding a fair, free election was "a necessary condition for our movement forward, to Ukraine's return to the European family of nations," and was confident about the ballot despite the bribery allegations.
"I'm sure that the election was well organized," Poroshenko said. "The expression of the will of the citizens will be protected."
The president's priorities persuaded schoolteacher Andriy Hristenko, 46, to vote for him
"Poroshenko has done a lot. He created our own church, bravely fought with Moscow and is trying to open the way to the EU and NATO," Hristenko said.
Ukraine's former prime minister, Tymoshenko, shaped her message around the economic distress of millions in the country.
"Ukraine has sunk into poverty and corruption during the last five years, but every Ukrainian can put an end to it now," she said after voting Sunday.
During the campaign, Tymoshenko denounced price hikes introduced by Poroshenko as "economic genocide" and promised to reduce prices for household gas by 50 percent within a month of taking office.
"I don't need a bright future in 50 years," said Olha Suhiy, a 58-year-old cook. "I want hot water and heating to cost less tomorrow."
A military embezzlement scheme that allegedly involved top Poroshenko associates as well as a factory controlled by the president dogged Poroshenko ahead of the election. Ultra-right activists shadowed him throughout the campaign, demanding the jailing of the president's associates accused in the scheme.
Zelenskiy and Tymoshenko both used the alleged embezzlement to take hits at Poroshenko, who shot back at his rivals. He described them as puppets of a self-exiled billionaire businessman Igor Kolomoyskyi, charges that Zelenskiy and Tymoshenko denied.
Many political observers have described the presidential election as a battle between Poroshenko and Kolomoyskyi.
Both the president and Kolomoyskyi relied on an arsenal of media outlets under their control to exchange blows. Just days before the election, the TV channel Kolomoyskyi owns aired a new season of the "Servant of the People" TV series in which Zelenskiy stars as Ukraine's leader.
"Kolomoyskyi has succeeded in creating a wide front against Poroshenko," said Vadim Karasyov, head of the Institute of Global Strategies, an independent Kiev-based think tank. "Ukraine has gone through two revolutions, but ended up with the same thing — the fight between the oligarchs for the power and resources."
