The liberal Yushchenko, favoured in the contest, has been bolstered by protesters in his orange colours who brought central Kiev to a halt for more than two weeks to back his charges of mass cheating in a 21 November poll.
He again faces Prime Minister Viktor Yanukovich, candidate of Ukraine's establishment, who says his victory last month was illegally taken from him when the supreme court threw out the result after the protests and ordered a re-run.
"I will win. That's 100%. I'm absolutely certain," Yushchenko, holding his youngest son in his arms, told reporters after casting his ballot in central Kiev on Sunday.
Backed by Russia, Yanukovich accuses his rival of trying to stage an "orange coup" on behalf of foreign powers.
Facing long odds, a beaming Yanukovich said at his polling station: "I expect the Ukrainian people to make the correct choice. I voted for our future, the future of the Ukrainian people".
Yushchenko favours integration
of Ukraine with western Europe
More than 33,000 polling stations in the country of 47 million people were due to remain open until 8pm (1800 GMT).
An exit poll was due to be released soon afterwards. About 12,000 foreign observers were monitoring the vote.
The ex-Soviet state has been buffeted by upheaval since Yanukovich was initially declared the winner.
After the supreme court annulled Yanukovich's victory, parliament approved a series of legal changes to eliminate electoral fraud and trim the powers of any future president.
On the eve of the new ballot, the constitutional court overturned some changes to allow voting at home for the infirm - a main source of cheating along with absentee ballots.
Officials said the vote was proceeding without difficulty.
Yanukovich warned he has no
control over his supporters
Yushchenko, his face still bearing the discoloured marks of dioxin poisoning he blames on authorities, described the last-minute changes as a "fly in the ointment" and his team said the effect on the vote would be minimal.
Yushchenko, a former prime minister and central banker, promotes an image of gradual integration with western Europe.
He has been careful to describe Russia as a strategic partner and appealed also to Russian-speaking voters in the east.
Outgoing President Leonid Kuchma, his 10 years in power marked by scandal, backed Yanukovich in the earlier vote but the prime minister now attacks him bitterly. Kuchma told reporters he hoped the campaign would now come to an end.
"Dear God, let this be the final vote. I'm sure it will be," Kuchma said, suggesting the loser concede within two days.
'What do we need? A
job, a salary on time, peace. That's it'
Ukranian coal miner
Turnout, just short of 20% at 0900 GMT, was slightly lower than in the two previous rounds.
"I hope this time we will make it work, though I feel people are divided," Lidia, walking with the aid of a stick, said after voting in Kiev, where support for the challenger is strong.
"I voted for a free, democratic Ukraine - Yushchenko, of course. I hope people like me will be cared for."
With the rivals eyeing each other with suspicion and given complicated appeals procedures, it was unclear when a winner could be officially declared.
Yanukovich warns he has no control over the "indignation" of his own backers, based mostly in eastern and southern areas.
In Donetsk, in eastern Ukraine's Donbass coalfield, the prime minister's supporters appeared resigned to the prospect of
a Yushchenko victory, but unwilling to put up stiff resistance.
"We are still working, just as we were. What do we need? A job, a salary on time, peace. That's it," said Leonid, a city miner. "They need power. They want it. They want only power."