Mr. Bolsonaro won a surprising 46%, just short of the 50% needed to win outright in the first round.
Brazil's far-right presidential candidate Jair Bolsonaro said on Monday he would stick to his hardline agenda on guns, crime and graft in the second round of the election due on October 28, alarming senior statesmen and human rights advocates alike.
Haddad, a former education minister and one-term mayor of Sao Paulo, had portrayed a vote for him as a show of support for Workers Party founder and former President Luiz Inacio Lula da Silva, whom many voters associate with good economic times and falling inequality.
Bolsonaro's victory in the first round is the latest in an alarming trend worldwide, as right-wing leaders with authoritarian politics have risen to prominence across Europe and the United States.
He was competing against those with more money behind them, greater media exposure and more traditional political support.
Bolsonaro's running mate, a retired general, has said military intervention can be justified to restore civic order and that Brazil's Constitution can be torn up and rewritten without input from citizens.
Before the vote, polls had given Bolsonaro a roof of about 40 percent; many analysts expected him to score no higher than 35 percent.
"There is a strong belief that in the Northeast region of Brazil, many of his voters were unable to vote for Bolsonaro as a result of electronic booth malfunction", Mario Balaban, a Brazilian Bolsonaro supporter living in New York City, told The Daily Wire.
This election result is, in large part, thanks to misinformation. Bolsonaro's own party - once a political afterthought - scored stunning gains, going from just eight seats to becoming the second largest party in the 513-member lower house, with 52 seats.
Ligia Torggler, a 58-year-old Sao Paulo retiree, said she entered the polling station thinking she would vote for Geraldo Alckmin, a traditional center-right politician.
Now Bolsonaro and Haddad, the two top candidates from a field of 13 on Sunday, will have to duke it out on October 28. And now it has failed to nominate a candidate who could appeal to conservative voters.
Bolsonaro is leading the polls in the first round of the presidential election, with 47 percent of the vote and 92.5 percent of the votes counted.
But his track record of fiery anti-democratic rhetoric, calls for police to kill as many criminals as possible, and offensive comments on women and minorities have alarmed former presidents and observers across the political spectrum.
Yet one-third of Brazilian voters - more than voted for Haddad - either stayed home, or cast blank or null ballots.
Voting Sunday revealed the deep divisions generated by Bolsonaro and Haddad.
But a Haddad voter, Jose Dias, said it would be a "catastrophe" if Bolsonaro triumphed.
Meanwhile, true to the Workers' Party's leftist roots, Haddad has promised to fight long-standing inequalities, scrap a major labor reform passed a year ago and invest more in education.
Nearly two-thirds of the electorate are concentrated in the more populous south and southeast of Brazil where its biggest cities, Sao Paulo and Rio Janeiro, are located - and where Bolsonaro holds a commanding lead.