Mandela, 20 years to the day of the late liberation leader's inauguration.
"We dedicate our victory to Madiba's memory, and pledge to continue taking forward his legacy and that of his peers and forebears," Zuma said on Saturday, using Mandela's clan name.
The party's 62.15 per cent share of the vote meant an
"overwhelming mandate" for a fifth term in government since the end of white-minority rule, Zuma said, speaking for the first time about the results.
Nostalgia for the father of the nation, who died last December, helped support for the ruling party in Wednesday's polls despite a series of corruption scandals, galloping unemployment and economic doldrums.
"The victory also reaffirms that the ANC remains the only true hope for the majority of our people, particularly the poor and the working class," Zuma said.
The results assure the ruling party 249 seats in the 400-member parliament, while main opposition the centrist Democratic Alliance's (DA) 22.23 per cent give it 89 seats.
New radical left-wing party the Economic Freedom Fighters (EFF) came third with 6.35 per cent, propelling its inflammatory leader Julius Malema into parliament.
Anti-apartheid veteran Mamphela Ramphele, a former World Bank managing director, garnered two seats for her Agang party after a disappointing performance.
Over 73 per cent of the 25.4 million registered voters cast their ballot.
A few thousand ANC supporters gathered in a square next to the party headquarters in Johannesburg on Saturday night for a victory party. Zuma danced on stage with party leaders while local artists performed amid flags and branding sporting the ANC's green, black and gold.
Zuma, 72, is assured of a second five-year term.
However, the ANC's support fell slightly from the 65.9 per cent it won in 2009 elections, as opposed to the DA's improvement on its previous tally of 16.66 per cent.
The DA also strengthened its position in the Western Cape province, the only governed by an opposition party.
The military deployed overnight Friday in Johannesburg's Alexandra township and police arrested 59 people for public violence after residents burnt tyres and barricaded streets over alleged voter fraud.
Rioting again flared briefly on Saturday night and police fired teargas to disperse a small group, according to spokesman Neville Malila.
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