Bolsonaro, a former army captain who has repeatedly expressed sexist, homophobic and racist opinions while supporting military dictatorship and torture, fell short of an outright victory by 4 percent in the first round of the elections and will face Haddad in an October 28 run-off.
He expressed confidence that Bolsonaro would easily win the presidency later this month, saying that many who voted for other candidates on Sunday want to block the PT, which held the presidency from 2003 to 2016, from returning to power.
Had he pocketed more than 50 percent, he would automatically have become the president-elect. Some recent polls have projected he could beat Bolsonaro in the second round.
All along, Brazilians have said their faith in leaders and their hopes for the future are waning.
Despite making several disparaging comments about the gay community, women and minorities which have appalled millions of Brazilians, his tough-on-crime posture, favourable remarks about Brazil's former military dictatorship and self-styled anti-establishment approach have appealed to many others.
"This was a great victory, considering we had no television time, a party that is still very small with no campaign money and I was in hospital for 30 days", he said in video streamed live over social media.
An exit poll also showed one of Bolsonaro's closest aides, former police Major Olimpio Gomes, scoring a surprise win in the Senate race in Sao Paulo state.
Front-runner Jair Bolsonaro, who some call a tropical Trump, has surged in opinion polls in the past week.
"A Haddad voter, Jose Dias, said it would be a "catastrophe" if Bolsonaro won the right to succeed unpopular outgoing centre-right President Michel Temer".
But Brazil is split over what cost to its democracy it may pay if it chooses Bolsonaro, a long-time congressman who has repeatedly praised the 1964-85 military regime but now vows to stick strongly to democratic ideals, a conversion many question.
At a news conference afterward, Haddad cast the second round as pitting Bolsonaro's "neoliberalism" against the social programs that the PT has promoted.
Bolsonaro has painted a nation in collapse, where drug traffickers and politicians steal with equal impunity, and moral rot has set in.
Haddad has also spent much time arguing that da Silva, his mentor, was unfairly jailed - a strategy aimed at attracting voters who still feel strong affection for da Silva, known in Brazil simply as Lula.
Meanwhile, true to the Workers' Party's leftist roots, Haddad has promised to fight long-standing inequalities, scrap a major labor reform passed past year and invest more in education.
"They should be prepared for all registered voters to turn up".
"I think we need a miracle", she said. "So I made a decision to vote for Bolsonaro, who is the only one who can block the return of the Workers' Party".
"A lot of young people are voting for him".