At 0730 GMT the rand was 0.13% firmer at 13.8225 per dollar, after closing at 13.8400 in the previous session.
The South African Reserve Bank (SARB) cut rates by 25 basis points to 6.5% in a unanimous decision, its first easing since March 2018, although it struck a cautious tone suggesting future reductions to borrowing costs were not a foregone conclusion despite benign inflation.
"The rand managed to hold its own again this week, trading in a tight range. Continuous carry trade remains one of the most prominent reasons for the rand's resilience," Bianca Botes, Treasury Partner at Peregrine Treasury Solutions said in a note.
Government bonds were firmer, with the yield on the benchmark 2026 instrument down 1 basis point to 7.965%.
On the bourse, stocks rose more than 1%, led by food producer Pioneer Food Group after U.S.-based beverage and snack maker PepsiCo made a takeover offer of $1.7 billion.
Shares on Pioneer surged 28.80% to 99.95 rand after the announcement.
The benchmark JSE Top-40 Index firmed 1.02% at 52,263 points while the broader All-Share Index rose 1.03% to 58,470 points.