At 1511 GMT, the rand traded at 13.8700 versus the greenback, 0.7 percent firmer than its previous close.
Stocks were broadly in the black, helping the country's benchmark index end the session more than 2 percent higher.
The rand's gains were linked to growing optimism that the world's two largest economies will strike a deal to avoid an all-out confrontation that would severely disrupt global trade, said Halen Bothma, a market analyst at ETM in Johannesburg.
"Market is still very much interested in a few big themes, one is the Fed, one is trade talks between China and the U.S. and the third, I would say, is global growth," he said.
Officials of the United States and China continued trade talks in Beijing for an unscheduled third day, amid signs of progress on issues including purchases of U.S. farm and energy commodities as well as increased access to China's markets.
On the bourse, the JSE Top-40 index ended 2.2 percent higher at 47,140 and the broader All-share index picked up 2.03 percent to 53,222.
In fixed income, government bonds also firmed, with the yield on the benchmark instrument maturing in 2026 down 1 basis point to 8.750 percent.
(Reporting by Tanisha Heiberg and Tiisetso Motsoeneng; Editing by Alexander Winning and Peter Graff)
