The unit is likely to have a quiet but firmer session on Monday with no data expected until Tuesday.
The rand was at 8.1330 at 0610 GMT, compared to a 8.1351 close on Friday. It needs to break through resistance around 8.1148, its 100-day moving average, to open up the big 8.06 barrier last hit in early July.
"Markets have rallied quiet hard on the back of the better-than-expected non-farm payroll data from Friday. All risk appetite is back on," said Brigid Taylor, head of institutional sales at Nedbank.
Offshore investors are buying local bonds after a sell-off two weeks ago. Yields were steady at Friday's closing levels, waiting for clearer moves from the currency but the bias was for lower yields in the session.
The 2015 yield was at 5.44 percent while the 2026 held at 7.275 percent.
"There's foreign demand again. We can expect to see support of the likes of South Africa and other emerging markets that offer value, and from that perspective we can expect the rand to remain relatively strong," Nedbank's Taylor said.
Early on Tuesday the central bank will release its latest reserves data. July numbers are expected to show slightly more gold and foreign exchange was accumulated by the Reserve Bank compared with the previous month. The data is due at 0600 GMT.