The rand gained around 1 percent against the dollar to trade at its best levels since June 2015, following reports that the ruling African National Congress (ANC) party plans to force Zuma to step down.
The rand has strengthened by about 12 percent since the election of businessman Cyril Ramaphosa as ANC leader in December, with investors warming to his promises to root out corruption and boost the economy.
"South Africa has a couple of things going for it which remind me of Brazil two years ago," said Kiran Kowshik, a strategist at UniCredit. Those include improving external balances, a shrinking current account deficit, high real yields and hopes of reform under Ramaphosa, he said.
"The momentum behind the reform expectations is very strong and will continue to support the rand. I don't think it's a big deal if it goes to 11.70 per dollar. The support is there for the currency," Kowshik said.
In another promising sign, Ramaphosa appointed a new board at state-owned power utility Eskom at the weekend. Eskom has been in a leadership crisis after several board members resigned in 2017 amid growing governance concerns.
South African bank stocks rallied hard, up 2 percent and the broader index rose 0.3 percent.
Shares of troubled South African retailer Steinhoff also jumped 10.6 percent after it announced a plan to sell $620 million of stock in investment firm PSG Group as it scrambles to plug a liquidity gap.
MSCI's emerging equity index rose 0.4 percent, underpinned by accelerating world economic growth. Equity markets are shrugging off the shutdown of the US government, after the Senate failed to reach a compromise on funding it .
"EM equities owe (their) strong performance to rising earnings," analysts at Goldman Sachs said it a note, adding that valuations had "significant room to improve" based on improving economic fundamentals and the rosier earnings outlook.
Chinese blue-chip stocks rose to 31-month highs.
In emerging Europe, Russian shares rose 0.7 percent, approaching Friday's record highs, as oil prices held near $69 a barrel.
But the lira weakened 0.3 percent after Turkey launched a military operation at the weekend against a US-backed Kurdish militia in Syria. The move threatens to further strain Turkey's ties with the United States.
The Romanian leu underperformed regional peers, trading at its weakest year-to-date against the euro. Tens of thousands of Romanians marched in Bucharest on Saturday to protest corruption and attempts by the ruling Social Democrats to weaken judicial independence.