This is in sharp contrast to Western governments which questioned the credibility of a rushed, disputed vote.
African monitors broadly approved the conduct of the election but Mugabe's main rival, Movement for Democratic Change (MDC) leader Morgan Tsvangirai, has said he will challenge the results in court with evidence of massive vote-rigging, irregularities and intimidation.
The sharply divergent views of Wednesday's vote surfaced after Zimbabwe's election officials declared a landslide win for Mugabe and his ZANU-PF party, giving Africa's oldest president five more years at the helm of a nation he has ruled for 33.
The standoff raises some fears the southern African nation risks repeating the turmoil that followed another contested vote in 2008. Election violence then forced Zimbabwe's neighbours to broker a shaky unity government between ZANU-PF and the MDC.
But Sunday's "profound congratulations" extended to Mugabe by Zuma, leader of Africa's economic powerhouse, reflected a willingness by the continent's diplomatic bodies to swallow the re-election of Mugabe, 89, for the sake of regional stability.
Mugabe, one of the grand old men of southern Africa's liberation fight that ended white minority rule, is admired as a defiant nationalist by some Africans, though others share the West's view of him as a ruthless despot who wrecked Zimbabwe.
"President Zuma urges all political parties in Zimbabwe to accept the outcome of the elections, as election observers reported it to be an expression of the will of the people," the South African leader said in his statement.
Zimbabwe's capital Harare was calm on Sunday, with many residents going to church. Newspaper billboards proclaimed "ZANU-PF gloats over victory", "Mugabe romps to victory" and "Tsvangirai disputes election results".
Western observers were barred from Wednesday's elections. Monitors from the African Union and the Southern African Development Community (SADC) who observed them made a point of stressing that they were peaceful, in contrast to the violence of 2008 polls, and also endorsed them as broadly free.
In contrast, the United States and European governments, which have sanctions in place against Mugabe over past election-rigging, listed a litany of alleged flaws in the vote, from lack of availability of the voters' roll to pro-Mugabe bias in the media and security services that skewed the election run-up.
In Zimbabwe, independent domestic monitors had described the election as "seriously compromised" by registration problems that may have disenfranchised up to a million people.
Anti-corruption watchdog Global Witness, citing links between mining companies, ZANU-PF insiders and Zimbabwe's pro-Mugabe military, has also alleged that state diamond revenues may have been spent on securing the Mugabe re-election.
ZANU-PF has angrily rejected all vote-rigging allegations. U.S. Secretary of State John Kerry spelled out Washington's distrust of the result in no uncertain terms.
"Make no mistake: in light of substantial electoral irregularities reported by domestic and regional observers, the United States does not believe that the results announced ... represent a credible expression of the will of the Zimbabwean people," he said in a strongly worded statement on Saturday.
Former colonial power Britain expressed "grave concerns". Foreign Secretary William Hague said the reported irregularities "call into serious question the credibility of the election".
The 28-nation European Union has also pointed to "identified weaknesses in the electoral process and a lack of transparency," completing a picture of general Western scepticism.
WHAT NOW FOR SANCTIONS?
It remained to be seen how energetically the West, with little public appetite at home for overseas interventions and facing muscular Chinese trade and investment rivaly in Africa, would press its questioning against the apparent African endorsement of the vote as imperfect but acceptable.
China is already a significant investor in Zimbabwe, which has rich reserves of chromium, platinum, coal and diamonds.
Mugabe had defiantly ignored a request by SADC in June to delay the election beyond July 31 to allow more time for steps to create a "conducive environment" for a free and fair vote.
At issue now will be the future of the Western sanctions against Mugabe and Zimbabwe, where the economy is still struggling to recover from a decade of slump and hyperinflation that ended in 2009 when the Zimbabwe dollar was scrapped.
Trevor Maisiri, senior analyst for southern Africa of the International Crisis Group, said the priority of the African Union and its regional satellites like SADC was avoiding conflict and civil strife. This often took preference over technical perfection in electoral processes.
"I don't think there is going to be any major social unrest. Some people are disappointed but they have already gone back to their lives," he told Reuters by telephone in Harare.
The MDC, facing political annihilation after its third failure to oust Mugabe through the ballot box, has said it could consider challenging Mugabe's win through street protests.
But this could trigger a crackdown from pro-Mugabe security services, militias and supporters. In the 2008 electoral violence, 200 MDC followers were killed in such a crackdown.
In Harare, after the tense, rushed weeks of electioneering, many seemed anxious to get on with their daily lives.
"The elections have come and gone, and people have different opinions about the outcome but we still need to pray for our welfare, for national peace," said one woman as she went into a service at the main Anglican Cathedral in the city.
"Politics is important, but it's not everything," she added, declining to give her name.