At 1500 GMT the rand traded at 18.3600 against the dollar, about 2% stronger than its previous close.
The dollar last traded about 1.1% weaker against a basket of global currencies.
U.S. consumer prices were unchanged in October amid lower gasoline prices, and underlying inflation showed signs of slowing, supporting views that the Fed was probably done raising interest rates.
"A softer inflationary impulse in the US... all but ends any remaining bets that the US Federal Reserve might still hike interest rates further in the current cycle," Danny Greeff, co-head of Africa at ETM Analytics, told Reuters.
If softer inflation is sustained, "it will also support the case for the Fed to take its feet of the brakes and gradually turn more growth-sensitive through the months ahead," he added.
Like other risk-sensitive currencies, the rand often takes cues from global drivers such as U.S. monetary policy as well as local data points.
Locally, South Africa's unemployment rate fell to 31.9% in the third quarter of this year from 32.6% in the second quarter, statistics agency data showed on Tuesday.
On the Johannesburg Stock Exchange, the blue-chip Top-40 index closed over 2.5% stronger.
South Africa's benchmark 2030 government bond was stronger, with the yield down 18.5 basis point at 10.230%.
(Reporting by Tannur AndersEditing by David Goodman, Bhargav Acharya, Alexandra Hudson)
