Private pollsters, approved by the national elections commission, are tabulating a sample of votes known as "quick counts". More than 80% of Indonesia's population professes Islam.
"Hopefully after today, the politics in Indonesia will calm again", she said.
Polls opened to a quiet start earlier in the day, but more voters started trickling to polling stations later in the morning and closer to lunchtime.
Mr Purnama won the first round, but not by enough of a margin.
The Indonesian rupiah weakened slightly after unofficial results were announced.
One Twitter user, @fuadhn, said Indonesians "can feel what United States and British citizens feel now".
Ahok's defeat is a setback for his political patron, President Joko "Jokowi" Widodo.
The chairman of Indonesia's biggest muslim organization Nahdlatul Ulama said on Tuesday (18/04) that voters in the Jakarta gubernatorial election should forget about the governor candidates' ethnic background when deciding who to vote.
National police chief Tito Karnavian has said thousands of police and military personnel would be deployed to secure the vote from intimidation.
Religious tensions have been an undercurrent in the campaign, with Basukion trial for blasphemy over comments he made a year ago that many took to be insulting to Islam.
The incumbent, Basuki "Ahok" Tjahaja Purnama is now on trial after allegedly insulting the Quran and hundreds of thousands protested against him in Jakarta, deriding his Chinese ancestry and calling for him to be imprisoned or killed. One person died and more than 100 were injured after one protest turned violent.
If Purnama - who won popularity for his determined efforts to clean up Jakarta - does win the vote and is then convicted of blasphemy, he would not automatically be barred from holding office and could avoid jail for a long time by filing successive appeals.
"It is forbidden under Islamic law, to have an infidel leader", he told Reuters.
(AP Photo/Tatan Syuflana). Indonesians queue up give their votes at a makeshift polling station under a bridge during the runoff election in Jakarta, Indonesia, Wednesday, April 19, 2017.
Despite the role of moderate Islam in the world's most populous Muslim country, the election raised tensions between Muslim and Christian communities in the capital, in part due to Purnama's blasphemy trial.
His platform has focused on improving public education, providing no-deposit home loans for low income groups and opposing a giant seawall in Jakarta Bay. Late previous year Islamic hardliners staged several massive protests in the capital, while discrimination has percolated through neighbourhoods across the capital.
Basuki congratulated his rival in a news conference.
Help us deliver news and views that matter to Malaysians. "We hope things don't heat up".
Purnama's bid for a second term has been dogged by a blasphemy case triggered by comments he made on the Quran that were deemed insulting to Islam.
Rising political tension ahead of Wednesday's election runoff is par for the course and should be seen as a sign that Indonesians are beginning to believe in the country's political processes, he added.
Officially a holiday for Jakarta residents, the Indonesia Stock Exchange is closed.
Three years ago, Malaysia Airlines flight MH370 disappeared from radar somewhere above the Indian Ocean with 239 people on board. Most worldwide flights use technology known as ADS-B, whose signals can be tracked from the ground or space.
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I mean you see. really?" "No, I said, 'I'd have to get back to you on that.' I think that he is still under audit". And he had previously suggested that the ex-businessman could offer those returns to the public on Tax Day.
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