Tymoshenko talked confidently after the poll, stating that Yanukovich would have no chance of victory in a second round and pushed for talks with eliminated candidates.
"As of today I am ready for talks so that we can move forward with uniting the democratic forces," she said.
Despite pre-election claims from both sides of vote-rigging, none of the main candidates have questioned the results.
The Organisation for Security and Co-operation (OSCE) said the poll was of "high quality" and "showed significatn progress over previous elections".
Joanna Gorska, deputy head of Eurasia Forecasting, Exclusive Analysis Ltd, told Reuters that Tymoshenko performed "probably better than expected".
She added the prime minister "is probably the most likely to eventually win" in the February 7 run-off "when you look at where the votes from the other candidates are likely to go to".
Sergey Tigipko, the former central bank chairman, was ranked in third place in the early results, with about 13 per cent of the vote.
| Yulia Tymoshenko, Ukraine's prime minister, still stands a chance in the run-off [AFP]
Voting closed at 18:00GMT on Sunday, and results have not brought the reaction seen in the last presidential election held in late 2004.
Then Yanukovich won an initial poll which led to protests over alleged fraud, instigating the so-called Orange Revolution.
The movement swept Viktor Yushchenko, the incumbent president, to power and created hopes of a new era of prosperity and European integration for the country of 46 million people bridging the EU and Russia.
But since then public disillusionment has grown over botched reforms and the political fracture between Yushchenko and Tymoshenko, both leaders of the Orange Revolution.
That disaffection appears to have left Yushchenko out of this year's race in the first round.
Hours before voting stopped, Al Jazeera's Neave Barker, reporting from Kiev, said voters had low faith in the fairness of the election.
"A recent poll suggested that only five per cent of the population believe this election will be free and fair, and I don't think the front runners have done much to inspire confidence over the last week of campaigning.
"The two leaders, Yanukovich and prime minister Tymoshenko, have accused each other of planning to rig the election.
"But that said, the same poll indicated that the voter turnout could be as high as 75 per cent. While people may be disillusioned with the political elite, they're certainly not apathetic."
After a campaign that saw the main protagonists trade insults, all the main candidates spent the final hours of their campaigns with appearances on Ukrainian political talk shows.
Yanukovich also held a glitzy rally in central Kiev attended by top Ukrainian pop stars.