Michelle Bachelet has promised major tax and education reforms to help ease Chile's social divisions after sweeping back to power with a huge majority in presidential elections on Sunday.

The centre-left candidate won with about 62% support, the highest share of votes for any presidential candidate since the country returned to holding democratic elections in 1989.

The landslide victory against Evelyn Matthei, the conservative candidate of the Alianza coalition, puts Bachelet back in the Moneda presidential palace after a four-year gap and gives her a mandate to push for an education overhaul and the fiscal reforms to help pay for it.

"Chile has looked at itself, has looked at its path, its recent history, its wounds, its feats, its unfinished business and this Chile has decided it is the time to start deep transformations," Bachelet told a jubilant crowd of supporters on Sunday night as confetti rained down. "There is no question about it: profits can't be the motor behind education because education isn't merchandise and because dreams aren't a consumer good."

Good-quality schooling is generally only available in Chile to those who can pay, and massive student protests demanding change hurt the popularity of the outgoing conservative president Sebastián Piñera. Bachelet ran on a platform of social policies to address a deep divide between rich and poor, and plans to raise the corporate tax rate. Chile, the world's top copper-exporting nation, is ranked the most unequal country in the 34-member Organisation for Economic Co-operation and Development (OECD).

"She will govern a country with profound demands for change," Senator Ricardo Lagos Weber of Bachelet's New Majority coalition told Reuters. "The country isn't flat on its back, it is healthy, organised, growing economically, creating jobs and improving salaries. But it is also deeply unequal."

Plans to change a constitution and electoral system that date back to Augusto Pinochet's 17-year dictatorship – which ended in 1990 – are also among Bachelet's campaign pledges.

"Bachelet has promised a lot and expectations are high, while the [economic] situation isn't as favourable as it was in recent years," said Patricio Navia, a political scientist and professor at New York University. If she does need to water down her promises because slower growth makes increased public spending tricky – or if opposition becomes obstructionist in a congress that remains divided after parliamentary elections last month – she could herself face popular protests.

Shortly after her victory on Sunday, hackers posted a message on the education ministry's website saying: "Mrs President we will take it upon ourselves to make things difficult for you. Next year will be a time of protests."

After expanding 5.6% last year, Chile's economy is ending 2013 with 4.2% growth and is expected to hit 3.75-4.75% next year. One of Bachelet's main economic policies is to reduce the effective fiscal deficit from about 1% of gross domestic product to zero by 2018, but a slowdown could make that target tough to hit.

Additionally, the US Federal Reserve is set to announce a pullback of its bond-buying programme with some investors expecting this to happen as early as this week. The programme has supported riskier assets such as commodities and equities and a tapering of the rate of purchases could heighten global volatility and borrowing costs for Chile and other Latin American states.

Bachelet's supporters say her reforms to boost tax revenue could help finance public spending even when growth slows. Among other things, the reform will look to progressively raise corporate taxes from 20-25%, bringing the rate closer to that of developed nations.

"A tax reform should have happened a long time ago to give resources to the state and to balance inequalities. But better late than never," said Carlos Huneeus, who runs the research centre Cerc.

Despite progress made by Bachelet's coalition in legislative elections last month, divisions in Congress mean her reformist aspirations will be subject to political wrangling. "Support from a few independent politicians in the senate and the lower house seems achievable, but the formation of a broader consensus will likely require the future president to compromise on some of the most controversial aspects of her agenda," said Tiago Severo at Goldman Sachs.

Last month, Bachelet's bloc clinched the simple majority it needs to pass tax reforms. But for the four-sevenths majority required for education reform, Bachelet will need to butter up independents or opposition legislators – from some of whom she has already received hints of backing.

Lagos, the son of the former president Ricardo Lagos, believes popular discontent can be harnessed to build support for the reforms. "We've never been better positioned than now to make reforms. I don't foresee an obstructionist opposition – that's going to have a high cost for them considering what people are demanding," he said.