With 82% of the votes counted after the poll on Sunday, Bachelet had 45.8% and Sebastian Pinera, a billionaire opposition candidate from the moderate wing of Chile's conservatives, was second with 25%.
Joaquin Lavin, another candidate from Chile's divided conservatives who have been out of power since Augusto Pinochet's 17-year dictatorship ended in 1990, ceded the election and said he would back Pinera in the second round.
"The people have spoken. That's democracy," said Lavin, who had about 23% of the vote.
If elected, Bachelet, a separated mother of three who was tortured under Pinochet, would extend the 15-year rule of a centre-left coalition that has cut poverty by half and overseen the country's transformation into the region's star economy.
Bachelet, a doctor and former defence minister, has pledged to overhaul Chile's private pension system and continue the liberal social programmes and free-market economic policies of Ricardo Lagos, the president.
Support for an agnostic, separated woman like Bachelet shows a marked shift in values in this the conservative, Roman Catholic country of 16 million people where divorce was legalised only last year and where machismo, or male chauvinism, is strong.
But Patricio Navia, a political scientist, said that Bachelet would have a tough fight in January.
"This is not good news for Bachelet," he said, noting that the combined total of votes for the two right-wing candidates exceeded those for Bachelet.
Other analysts have said that not all of Lavin's supporters could be counted on to vote for Pinera in a second round.
Even so, Bachelet's centre-left bloc was also seen taking firm control of both houses of Congress in parliamentary elections that also took place on Sunday.