Stocks ended slightly lower, led by retailers Massmart and TFG after the duo reported weaker financial results.
At 1530 GMT, the rand had firmed 0.54 percent to 12.8550 per dollar, its firmest since March 30, compared with a close of 12.9250 in New York on Wednesday.
Traders said the rand was also maintaining the positive momentum from the previous session after inflation slowed faster than expected.
"It is not often that a lower inflation print, which indicates lower interest rates, translates into a stronger currency but that is pretty much what happened yesterday," Standard Bank chief currency trader Warrick Butler wrote in a note.
"It continues to show how desperate the market is for yield and the fact that we may start seeing rate cuts in South Africa sooner rather than later caused a flood of bids for local paper and this subsequently caused the rand to strengthen."
South Africa's central bank kept interest rates steady on Thursday, as it weighed price pressures against expectations that the struggling economy will recover more slowly than hoped.
In fixed income, the yield for the benchmark government bond due in 2026 rose 1 basis point to 8.51 percent.
On the bourse, the JSE Top-40 index lost 0.52 percent to 47,572 and the broader All-share index was down by the same margin at 54,028.
Massmart slumped 6.7 percent after the unit of the unit of Wal-Mart Inc said same-store sales fell 2 percent in the first five months of the 2017 fiscal year.
Apparel retailer TFG also featured on the losers' list, dropping 5.7 percent after reporting a below-forecasts full-year profit growth.
Overall, a stronger rand weighed on broader sentiment, hitting heavily weighted mining stocks such Impala Platinum , Gold Fields and Anglo American, traders said.