Incumbent left-leaning President Dilma Rousseff of the Workers Party (PT) faces centrist Aecio Neves of the Brazilian Social Democracy Party (PSDB) in the second run-off round.
Both candidates have pledged to kick-start Latin America’s largest economy and make it more competitive.
Voting opens at 08:00 (10:00 GMT).
The latest opinion polls showed President Rousseff with a slight lead over the opposition candidate.
A survey by pollster Datafolha gave her 52% voter support against 48% for Mr Neves.
A separate survey by polling firm Ibope gave the incumbent 53% against 47% for her challenger.
Both polls had a margin of error of plus or minus 2%.
Battle for middle class
Poor Brazilians, particularly in the impoverished northeast, remain loyal to Dilma Rousseff thanks to her party’s trademark welfare programmes, such as the Bolsa Familia family grant scheme.
She obtained her largest support there in the first round of the presidential election on 5 October, with almost 60% of votes.
But wealthy Brazilians, who are against interventionist economic policies such as petrol price controls and high taxes, favour instead business-friendly Aecio Neves.
He is regarded in the financial markets as someone to put the economy back on track, after four years of low growth rates with the country now technically in recession, says BBC Brasil’s Julia Carneiro.
More than 140 million Brazilians will vote on Sunday, but correspondents say much will depend on who wins the middle-class vote in the industrialised southeast.
Nowhere is the race closer than in the southeastern state of Minas Gerais where the two candidates were both raised, the BBC’s Wyre Davies reports.
On Saturday, Mr Neves campaigned in his native state, where he served two terms as governor, and paid a visit to the grave of his grandfather Tancredo, who was elected president in 1985 but died before taking office.
Ms Rousseff, who has been serving as Brazil’s first woman president since 2010, spent instead the last day of campaigning in her southern stronghold of Porto Alegre, the capital of Rio Grande do Sul, where she held a rally.
The vote is widely seen as a referendum on 12 years of government by her Workers Party.
Dramatic race
The PT came to power in 2002 with Luiz Inacio Lula da Silva as president.
Its policies are credited with lifting an estimated 40 million Brazilians out of extreme poverty.
But President Rousseff’s government has faced allegations of corruption and of overspending in preparations for this year’s football World Cup.
She also presided over rising inflation and a recession this year.
The election comes after weeks of intensive campaigning by the two candidates and a presidential race that turned dramatic after Eduardo Campos, a main opposition candidate, was killed in a plane crash in August.
His running mate, a renowned environmentalist, Marina Silva, was thrust into his spot, vowing to become the South American country’s first “poor, black” president.
But she came third in the first round after Ms Rousseff and Mr Neves secured 41.5% and 33.5% of the vote respectively.
As neither candidate got an absolute majority, the election went into a second round.
Ms Silva has backed Mr Neves in Sunday’s runoff vote. (BBC)
