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The near-threefold increase was compared with the June quarter, seasonally adjusted and annualised.
Stats SA said the sector recovered largely on account of easing local and global lockdown restrictions.
Production had plunged 47.3% year-on-year in April during the national lockdown to address the spread of COVID-19 but started showing signs of recovery from July.
"Higher production was mainly due to increased activities in the production of platinum group metals, iron ore, gold, manganese ore and diamonds," Stats SA said of the third quarter figures.
The country's GDP increased at an annualised rate of 66.1% for the period, or by 13.5% quarter-on-quarter seasonally adjusted.
Mineral resources and energy minister Gwede Mantashe said he was encouraged by mining's performance in the third quarter.
"These are the results of the dynamic engagements we had with all stakeholders in the sector as the country went into a nationwide lockdown in March this year," he said.
"We came up with a programme to save the industry together, whilst saving lives and protecting livelihoods."
However he warned more effort was needed.
"We must continue working together as stakeholders for the sector to do even better and take a step closer to an ambitious target of the sector contributing 12% to the GDP and attract 5% of exploration investment," he said.
He also stressed safety was a priority, following news two weeks ago there had been 52 fatalities so far this year in the country's mining sector, one more than the record low in 2019.
"Workers must be able to go underground and be assured of coming back alive," Mantashe said.