An early count is expected overnight on Monday.
The opinion polls predict a humiliating defeat for Poroshenko, who came to power five years ago with 55 percent support after a deadly pro-West uprising removed his Russia-backed predecessor Viktor Yanukovich in 2014.
He has been projecting himself as Ukraine’s passionate commander-in-chief since the so-called Revolution of Dignity resulted in the war between Moscow-backed separatists in Donetsk and Luhansk regions, and the Ukrainian army. The conflict has killed more than 13,000 people.
During the election campaign, Poroshenko told Ukrainians that Zelensky would fail to protect them from Russia’s President Vladimir Putin.
Svitlana Kravchenko, 62, told Al Jazeera in Kiev that Poroshenko might have made mistakes over the last five years, but his achievements should not be overlooked.
“He secured the independence of Ukraine’s Orthodox Church from Moscow, visa-free travel agreement [with the European Union and many other things that everyone knows about,” she said. “Who doesn’t make mistakes? Everyone does. But his main course is right.”
Nataliia Sytnyk, 59, also voted for the incumbent despite her doubts about him.
“[Poroshenko] appeals to me because he has some weight on the international arena,” she told Al Jazeera. “But if Zelensky wins, it will not be a tragedy for the country because the important thing is that our country is already on the right path.”
But the majority of the population holds Poroshenko responsible for the government’s failure to tackle endemic corruption and deteriorating living conditions.
Volodymyr Hryhorovych, 70, said Poroshenko’s government was corrupt to the core and Ukraine needed a complete overhaul of the system.
“I voted for Zelensky in both rounds, because [under Poroshenko] five years have passed and almost nothing changed. With Zelensky, at least there is hope that this new authority will not be corrupt.”
More than 72 percent of voters are expected to support the comic, who has been playing a corruption-busting president on TV for the last three years.
In the first round of voting held on March 31, Zelensky came first among 39 presidential candidates with more than 30 percent of ballots – double what Poroshenko secured.
The millionaire comic of Jewish descent benefited from the support of Ukrainians seemingly tired of mainstream politicians.
The father of two from the industrial city of Krivy Rig in central Ukraine has shunned campaign rallies in favour of comedy shows, and prefers to get his message across through YouTube clips and social media updates.
Many people fear if Zelensky becomes president, the country will be run from the shadows by self-exiled oligarch Ihor Kolomoisky.
Kolomoisky, who has been living in Israel since Ukraine started investigating alleged financial wrongdoings in his now-nationalised PrivatBank, owns the television channel that airs Zelensky’s shows.