The world's third-largest listed oil firm by market value said strong refining margins and higher oil prices, which hit a record of over $70 per barrel during the quarter, had more than compensated for production losses caused by US hurricanes.
The profit was boosted by one-off gains of $1.569 billion, mainly related to the sale of an interest in Dutch gas distributor Gasunie.
Shell's London-listed "A" shares were up 0.9 percent at 1,705 pence at 1427 GMT, when the DJ Stoxx European oil and gas sector index was down 1.7 percent.
"We captured the benefit of high oil and gas prices and refinery margins, even after the impact of hurricanes in the US," Chief Executive Jeroen van der Veer told a conference call with journalists.
Shell said its current cost of supply (CCS) net profit, which strips out gains from rises in the value of fuel inventories, rose 68 percent to $7.369 billion.
Excluding the one-off gains, Shell's "clean" CCS profit - the measure forecast by analysts and most closely watched by investors - was $5.8 billion.
"CCS is much better than expected ... We are positively surprised that the impact of hurricane costs is lower than anticipated," Margarita Shevtsova, analyst at Bank Oyens & van Eeghen said.
Shell's net profit is almost double the $4.8 billion figure larger rival BP Plc notched up in the third quarter but was pipped by the $9.9 billion net profit reported by Exxon Mobil on Thursday.
Shell, one of the largest producers in the Gulf of Mexico, was hard hit by hurricanes Katrina and Rita when they battered the Gulf in August and September respectively.