"We knew that it would be tough to win on the first round, we worked really hard, and we almost did it," she told supporters.
"We did win tonight, and we are going to work hard to win comfortably in December."
Bachelet, Chile's first woman president who worked as the head of UN Women after her first term in office, is now eyeing a potential non-consecutive second term as leader of the South American nation with the highest per capita income.
Since Bachelet, who is seeking to succeed conservative billionaire President Sebastian Pinera, did not top 50 percent of the ballots, a run-off -- also the country's first between two women -- was set for December 15.
"I am really pleased. We will have a runoff," Matthei told reporters.
Matthei and Bachelet were trailed by independent economist Franco Parisi and Socialist Franco-Chilean filmmaker Marco Enriquez-Ominami, at about 10 per cent each, returns showed.
A pediatrician by training who was Chile's first woman president from 2006 to 2010, Bachelet wants to overhaul the country's political and economic system, a legacy of Augusto Pinochet's 1973-1990 military dictatorship.
The 62-year-old wants to make abortion legal, and to raise business taxes to offer free university, answering the demands of a powerful student movement that led a series of massive protests since 2011.
The daughter of an air force general and a separated mother of three, Bachelet is supported by a "New Majority" alliance of socialists, Christian Democrats and communists.
As girls, Bachelet and Matthei played together on a military base in Chile's parched north.
Chile has the highest GDP per capita in Latin America -- USD 22,362 based on purchasing power parity -- but half of the nation's 17 million people make less than USD 500 per month.
Balloting generally went smoothly, though a group of protesting students occupied Bachelet's campaign headquarters calling for election reform. There were no immediate reports of damage or injury, however.
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