But anger was mounting over obstacles faced by Romanians trying to vote abroad in the second-round runoff, where a large turnout could threaten a Ponta victory.
The election is seen as pivotal for one of the poorest countries in Europe which has struggled to combat an entrenched culture of public corruption.
A victory for Ponta, 42, would make him Romania's youngest ever president and cement his Social Democrat party's hold on power in the former communist state.
Ponta headed into the second round of voting with 54 percent support, according to the latest opinion polls, clearly ahead of his conservative opponent Klaus Iohannis.
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In the first round on November 2, Ponta took 40 per cent of the vote against 30 percent for Iohannis.
But 46 per cent of the ballots cast abroad were for Iohannis compared to just 16 percent for Ponta.
First results are expected overnight from the seventh presidential election since the fall of dictator Nicolae Ceaucescu 25 years ago.
Ponta has support from the hugely influential Romanian Orthodox Church, as well as his party's traditional electorate of the rural population, small business employees and the eldery and has been able to count on generally steady economic progress.
However, the economy fell into recession in the second quarter of 2014, although the government is forecasting 2.2 percent growth over the year.
Casting his ballot, he said he hoped Romania would "enjoy respect and prosperity".
Rodica Avram, a 56-year-old teacher, said after casting her ballot in Bucharest that she had voted for change.
"For the past 25 years we have heard nothing but lies and promises that weren't kept," she said. "I hope we'll finally have a president who respects people and does what he promises.