But pundits believe Pinera, a conservative 67-year-old billionaire who was president from 2010 to 2014, may not gain enough support to avoid a runoff next month -- likely against Alejandro Guillier, an independent supported by Bachelet's Socialists.
Chile's constitution bans consecutive terms for presidents, but re-election after skipping a term is permissible.
Bachelet herself led the conservative South American country -- Latin America's fifth-biggest economy -- from 2006 to 2010 and then was re-elected to replace Pinera in 2014.
"It's not very likely" he will get the 50 per cent or more of ballots needed to avoid a run-off, said political analyst Mauricio Morales of Talca University.
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In that case, a second-round showdown would be held between the top two candidates on December 17, and the winner would take over the presidency in March 2018.
Bachelet, who was also Chile's first woman president, hugged and took photographs with female supporters before casting her vote in Santiago.
Pinera, 67, also cast his vote in the capital.
"Chileans are going to make a decision that will affect our lives for many decades," he said.
Guillier, a 64-year-old former state TV anchor turned senator who presents himself as an independent, has 25 per cent of voter support against 44 per cent for Pinera, according to opinion polls.
With the outcome weighted heavily in Pinera's favor, voter apathy could be an issue -- even though there are six other candidates in the race beyond the top two.
"People don't want to vote because, really, nobody believes there will be any significant change anywhere. Also, they see who will be president as a foregone conclusion," said Catalina Gascone, a 19-year-old student.
Analysts predict that abstention could be as high as 40 per cent, and that Pinera has more motivated voters who will turn out.
On the other hand, it is the first poll in the country's history that includes expatriate citizens, with some 40,000 Chileans out of an estimated 850,000 living abroad expected to cast their ballots.
But a Pinera comeback is not seen as a rejection of the overall economic and social model erected in the Bachelet years, during which Chile posted annual growth of 1.8 per cent and passed tax and labor reforms, an introduction of free education, and the right to abortion.
"Chileans don't want to tear down the model, just fix its structure," Morales said.
Pinera has promised modifications to Bachelet's reforms, as well as vowing to have Chile join the club of developed nations within eight years.
"He is not going to have a majority in Congress," analyst Marta Lagos, founder of Latinobarometro and MORI Chile, predicted.
Today's balloting also includes legislative elections for many congressional seats.
Electoral forecasts suggest the right will increase its representation, but will probably not have the majority in either chamber.
Polls opened at 8:00 AM and are scheduled to close at around 6:00 PM. First results are expected about 90 minutes later.