At 5pm, the rand bid at R11.7896 to the dollar, 3.02cents firmer than at the same time on Monday.
Trump said on Twitter he was replacing Tillerson with Mike Pompeo, the director of the Central Intelligence Agency, and that Gina Haspel would take over from Pompeo.
The dollar was also held down by news of slowing US inflation, suggesting that the Federal Reserve remained on track to raise interest rates at a gradual pace.
The rand barely reacted to local data showing manufacturing output rose 2.5percent in January, supporting market views that the domestic economy retained momentum at the start of the year.
The currency has largely stayed at elevated levels in recent months, buoyed by expectations of faster economic growth under the new political leadership.
“Hopes for a political change have been spurring the rand higher since November. However, the air should be getting thinner for further surges of the rand as the new government will have to ‘deliver’ now,” Commerzbank analysts wrote in a note.
“We expect a moderate rand depreciation trend in the coming months.”
In fixed income, the yield for the benchmark government bond due in 2026 rose 3 basis points to 8.095percent, reflecting weaker bond prices.
In the equities market, stocks were a little volatile on the day, often changing from red to black and red again as they tried to find a fresh catalysts.
The JSE all share index dropped 0.19percent to 59084.51 points, while the Top40 index edged down 0.13percent to 52371.5 points.
Crisis-hit retailer Steinhoff closed down 3.41percent to R4.25 after it said it had sold its 17percent stake in KAP Industrial for R3.66billion, another step in its efforts to shore up its finances and pay down debt.
KAP shares fell as much as 4 percent before recovering to close slightly up 0.47percent to R8.54.
“The market was thinking that they would sell their whole stake. Maybe the market takes it as a positive,” said Cratos Capital trader, Greg Davies.
Still reeling from a move by Trump to impose tariffs on US metal imports, ArcelorMittal retreated 9.47percent to R2.58.