(Adds approval confirmation, finance minister comment)

By Rosalba O'Brien

SANTIAGO, Sept 10 (Reuters) - Chile's Congress approved President Michelle Bachelet's tax reform bill on Wednesday evening, the first key part of the center-left leader's tax-and-spend campaign pledge to reduce inequality.

The reform, which will increase the cost of doing business in Chile by raising corporate taxes and closing some tax exemptions, had been fiercely opposed by right-wing politicians and business leaders, who say it will crimp investment at a time when economic growth is slowing.

The government says the extra cash it will bring in - equivalent to about 3 percentage points of gross domestic product by 2018 - is needed to pay for an overhaul of Chile's education system and other social reforms.

"This emblematic tax reform of President Bachelet...will allow us to sustainably finance the other reforms," said Finance Minister Alberto Arenas during the final debate.

The passing of the bill into law is Bachelet's biggest political success since she returned to the presidency of Chile after winning last year's election in a landslide.

Approval was rarely in doubt since Bachelet commands a working majority in both houses of Congress. The reform was passed by a wide margin but the backdrop has been more complicated than the government had predicted.

The president's popularity has ebbed away as the economy has weakened, other reforms have stalled, and the country's security situation has deteriorated after a string of attacks sometimes blamed on anarchists.

REFORM OPPOSITION

The tax reform was first submitted to Congress in March, in a whirlwind of government activity less than a month after Bachelet took power.

It was approved largely unchanged, although some tweaks had been made to appease opposition lawmakers and doubters within Bachelet's own bloc. The government has said it wants a consensus to ensure the reform's future longevity.

However, not everyone is happy. An Adimark public opinion poll published last week showed that more people now disapprove of the tax reform than approve of it, a reversal of earlier attitudes that reflects worries about the economy as well as the success of the opposition warnings.

Most Chileans do not really understand how the tax reform affects them, said political analyst Guillermo Holzmann. "Getting the tax reform out is a political success," he said. "It then needs to be explained to the public, who wants more clarity on what those changes mean."

For a FACTBOX on the tax reform, please see (Additional reporting by Antonio de la Jara; Editing by Andrew Hay and Lisa Shumaker)