Full results are expected on Monday.
An exit poll placed Sandu on 54.8% of the vote against 45.2% for Dodon.
The West and Russia are vying for influence in the former Soviet republic of 3.5 million people, which is one of the poorest countries in Europe and suffered a severe economic recession during the COVID pandemic -19.
As the results arrived on Sunday evening, celebrations erupted outside the opposition headquarters in the center of the capital Chisinau, with supporters chanting “President Maia Sandu” and “a country for young people”.
Addressing his supporters, Sandu vowed to unite the country and fight corruption.
“We need the state to work for the citizens, not for thieves and corrupt officials,” she said.
Dodon, who had called on his supporters to take to the streets on Friday if he felt the election had been stolen from him, said on Facebook: “I urge everyone to calm down, regardless of the election results. »
Opinion polls had put rivals neck and neck before the second round of the elections. Sandu finished first in the first round two weeks ago with a late surge of support from voters living abroad, but failed to secure enough votes for an outright victory.
On Sunday, more than 200,000 Moldovans living abroad voted in the early evening, against a total of 150,000 in the first round.
Known for her tough stance on corruption, Sandu last year led a short-lived government that was overthrown in a vote of no confidence.
Sandu, 48, said she would get more financial support from the EU as president. Dodon, 45, has been in power since 2016 and has announced that he will roll out a settlement next year for the breakaway Russian-speaking region of Transnistria.
“I voted for the development of the economy, for a balanced foreign policy,” Dodon said after voting. “I don’t want Moldova to be used in geopolitical games.”
If Sandu wins, she will likely seek early parliamentary elections to consolidate power as the parliament is controlled by Socialists, Dodon’s former party.
Moldova, wedged between Ukraine and EU member Romania, has suffered from political instability over the past 10 years. Romanian President Klaus Iohannis said he was “happy” with Sandu’s first-round victory, while Russian President Vladimir Putin last month called on Moldovans to vote for Dodon and that there were long lines of waiting at polling stations in Moscow on Sunday.
The EU reached an agreement on closer trade and political ties with Moldova in 2014, but has become increasingly critical of its record on reforms.
Sandu has received messages of support from German Defense Minister Annegret Kramp-Karrenbauer and former European Council President Donald Tusk. Some of Dodon’s supporters denounced this support as an attempt to destabilize Moldova.
Sergei Naryshkin, the head of the Russian foreign intelligence service SVR, accused the United States last month of plotting to spark mass protests against Dodo as punishment for maintaining good relations with Moscow.
“Maia Sandu’s second round victory would signify a period of difficult political confrontation for Moldova,” independent analyst Corneliu Ciurea told Reuters news agency.