At 1454 GMT, the rand traded at 14.1425 against the dollar, roughly 0.5% firmer than its previous close.
President Cyril Ramaphosa announced the loosening of restrictions in a televised address on Sunday, shortening a nationwide curfew and extending the hours of alcohol sales as new infections decline.
South Africa has been the worst-hit on the African continent in terms of reported COVID-19 cases and deaths, with its economic recovery hampered by a slow start to its vaccination campaign.
This week, domestic investors will look to mining figures for June and July as well as July retail sales for clues about the pace of that recovery. Globally the focus is on U.S. economic data releases that could be crucial to the Federal Reserve's decision on when to exit its super-supportive policy.
Shares on the Johannesburg-based stock exchange were lifted as the government eased local restrictions, and Wall Street, on which almost 80% of the local market is indirectly linked, stayed upbeat.
The benchmark all-share index went up by more than half a percentage point to end the day at 64,652 points and the blue-chip index of top 40 companies closed up 0.55% to 58,495 points.
The market was lifted by mining companies with the resources index up 1.77%. The local economy-linked stocks such as banking and financials added to the gain with the bank index closing up 1.18%.
However, the star performer of the day was Sasol Ltd, the world's biggest producer of motor fuel from coal, which clocked almost 8.5% on Monday on stronger crude prices.
The yield on the government's benchmark 2030 bond was up 4 basis points to 8.895%, reflecting a lower price.
(Reporting by Alexander Winning and Promit Mukherjee;Editing by Bernadette Baum)
