SAO PAULO, Brazil (CNN) -- A close ally of President Fernando Henrique Cardoso appears to have won a runoff for the governorship of Brazil's most populous state Sunday, which could help the president push through unpopular austerity measures needed to prop up the country's shaky economy.

However, exit polls by the respected Ibope organization showed Cardoso allies going down to defeat in several other states, where new governors could prove to be thorns in the president's side.

The first actual ballot tallies weren't expected until Monday.

In Sao Paulo state, with 30 million people and an economy nearly as large as Argentina's, incumbent Gov. Mario Covas took 56 percent of the vote in a runoff against right-wing populist Paulo Maluf.

In Rio de Janeiro state, Anthony Garotinho, a radio announcer from the center-left Democratic Labor Party, was projected to take 59 percent of the vote, easily besting a Cardoso ally, Cesar Maia, the former mayor of Rio city.

In the southern farm state of Rio Grande do Sul, leftist Workers' Party candidate Olivio Dutra narrowly wrested the governorship from incumbent Antonio Britto, a Cardoso backer.

In Minas Gerais, former President Itamar Franco, a Cardoso critic, took 59 percent of the vote, easily ousting incumbent Gov. Eduardo Azevedo, a member of Cardoso's party.

In the Federal District, which includes the capital, Brasilia, Cristovam Buarque of the Workers' Party narrowly beat conservative former Gov. Joaquim Roriz, Ibope's polls showed.

Sunday's runoff elections for 13 state governorships were important because many of Cardoso's austerity proposals will require congressional approval, and governors have tremendous influence over how legislators vote.

Indeed, Cardoso considered the race for the Sao Paulo governorship so important that he delayed announcing sweeping tax increases and budget cuts to avoid hampering Covas' chances in Sunday's ballot.

Covas, 68, has won praise from economists for putting Sao Paulo's financial house in order. He restructured the state's huge debt by dismissing more than 100,000 civil servants and selling inefficient state-owned businesses.

In a bid to win international help for Brazil's struggling economy, officials from the International Monetary Fund and Cardoso's administration have been working on a plan to slash Brazil's $65 billion deficit.

Brazil is a victim of the global financial crisis that began last year in Asia and shifted to Russia before hitting Latin America. The crisis already has prompted a flow of money out of the country, some $25 billion in the past two months alone.

Races in 14 other Brazilian states were decided in the first round of voting October 4. Cardoso also won the majority he needed for re-election in that first vote.

While voting is mandatory in Brazil, observers said the turnout appeared to be low Sunday, with voters subdued.

Reuters contributed to this report.