The claims drew hundreds of thousands of conservative Muslims onto the streets of Jakarta in major protests past year, and Purnama has been put on trial in a case criticised as unfair and politically motivated.
The Jakarta poll has been overshadowed by religious tensions, with Islamist-led protests against Governor Basuki Tjahaja Purnama, an ethnic Chinese Christian, and calls for voters to choose a Muslim leader for the city.
He has not been barred from running but his lead in opinion polls was dented for a period, and analysts and the public are viewing the vote as a test of whether pluralism and a tolerant brand of Islam in the world's most populous Muslim-majority country are being eroded.
Mr Purnama, or "Ahok", is the first Christian and minority ethnic Chinese leader of Jakarta in over 50 years.
Police deployed 75,000 personnel across Indonesia with 16,000 in Jakarta, concerned hardline Muslim groups may again take to the streets to oppose Purnama. Purnama, or Ahok as he is commonly known, is running against two Muslim candidates and the vote is widely expected to go to a second round.
He denies the charge.
Baswedan, who urged Islamic voters throughout his campaign not to support a non-Muslim leader, said his message in the second round would be more focused on politics.
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Yudhoyono, an Army major until he resigned to run, is the eldest son of Susilo Bambang Yudhoyono, a former president. Purnama was a deputy to President Joko Widodo when he was the previous Jakarta governor and Widodo's party is backing him.
His main rival, former education minister Anies Baswedan, is backed by a retired general, Prabowo Subianto, who is promising a comeback to the national stage after losing to Widodo in the 2014 presidential vote. "Today, we saw that the majority of Jakarta's residents believe that Ahok-Djarot can provide social justice to all", Ahok said in a press conference at Rumah Lembang, his gubernatorial campaign headquarters, in Central Jakarta on Wednesday (15/01).
The vote is one of the 101 regional elections to be held simultaneously across the archipelago, but has hogged all the attention. However, the tenacity of Incumbent Governor Basuki Tjahaja Purnama, who bounced back from the apparent political death sentence of blasphemy charges and a trial, means he could still eke out a victory. "Ahok did good actually, but I'm voting for someone with the same faith as me".
Polling stations will close by 0600 GMT.
Former education minister Baswedan had secured 40.54 percent of the votes, just ahead of Purnama in second place with 39.43 percent, based on a quick sample count of around 10 percent of the vote by a private polling firm SMRC.
An early vote tally released in the afternoon should give an indication of how the candidates have performed although official results will not be announced for several weeks.