Ms Bachelet, 54, is an atheist singe mother who is trained as a paediatrician and had served as defence minister.
She fell just short of the 50 percent needed to avert a January 15 run off ballot, taking 45,9 percent, more than 20 points ahead of conservative Sebastian Pinera, according to an official tally.
“We are facing a historic event: a woman at the helm of Chile,” Ms Bachelet told supporters in Santiago.
“We will win in the second round because there is no going back,” she said.
She is running for the centre-left Concertation coalition that has governed Chile since General Augusto Pinochet’s dictatorship ended in 1990.
“Not even all the money of the candidate of the right will change the outcome of the second round,” she said, referring to Mr Pinera, who is one of the country’s richest men.
The results mirror opinion polls that indicated Ms Bachelet would dominate the presidential election but it would go to a run-off.
Ms Bachelet has pledged to pursue the successful policies of outgoing president Ricardo Lagos, a fellow socialist who won praise for his management of South America’s star economy.
If she wins, she would be the first woman to lead Chile.
Her turbulent and painful family history clearly struck a chord with voters and connected her to many Chileans.
Her father, a general, was arrested when Pinochet gained power in 1973, and died six months later, weakened by torture.
She was arrested two years later with her mother and suffered torture while in prison.
The pair fled to Australia to escape the brutality of the Pinochet regime, where they gained asylum, later moving to East Germany.
The three main presidential candidates all support the free market policies that have built Chile into one of the most prosperous economies in Latin America.
With hot, sunny weather in most of the country, turnout was heavy for the fourth presidential election since Chile restored democracy after the 1973-90 dictatorship of General Augusto Pinochet.
Voting is mandatory, but fines are rarely imposed on those who fail to cast ballots.
Polls started closing gradually about 4.30pm local time but some had to remain open to allow those in line to vote.
The first poll to close was one with 48 registered voters at an air force in Antarctica.
Only a few, minor disturbances were reported.
The 8.2 million registered voters were also electing one half of the 38-member Senate and all 120 member of the lower house of congress.
After months of sometimes bitter rivalry, Mr Lavin and Mr Pinera agreed on the eve of the vote that whichever finishes second to Ms Bachelet would be supported by the other in a runoff.
The successor to Socialist President Ricardo Lagos will be sworn in on March 11 for a four-year term.
Mr Lagos, who is ending his term with an approval rate of over 70 per cent, stood in line for 20 minutes to vote at a crowded public school near the presidential palace.
“We have worked to make Chile even more democratic and to ensure that we maintain economic growth and that the growth reached all Chileans,” he said.
Reduce wealth gap
All three leading candidates have insisted they will stress efforts to reduce the gap between the rich and the poor, curb the eight percent unemployment rate and the rising crime in large cities.
They say they aim to improve the current economic model, not change it.
The election confirmed that Chileans have put the legacy of General Pinochet behind them.
The 90-year-old former dictator played no role in the campaign.
He was not even able to cast a vote as he remained under house arrest, facing human rights and corruption charges.
If elected, Ms Bachelet would be the fourth woman to win a direct popular election as president in the Americas after Nicaragua’s Violeta Chamorro, Panama’s Mireya Moscoso and Guyana’s Janet Jagan.
She would be the first of those who did not rise to prominence because of her husband.
Other women have held presidential power after serving as vice presidents or when chosen by legislatures.
Several women also have served as prime ministers after their leading parties to electoral victories, notably Eugenia Charles of Dominica and Maria Liberia-Peters of the Netherlands Antilles.