After rising to 30,524.53, the 30-share index was trading at 217.69 points or 0.72 per cent higher at 30,413.86.
Similarly, NSE Nifty rose 57.70 points, or 0.65 per cent, to 8,936.80.
ITC was the top gainer in the Sensex pack, surging around 3 per cent, followed by L&T, Tata Steel, NTPC, HUL, PowerGrid, HDFC twins and UltraTech Cement.
On the other hand, Hero MotoCorp, IndusInd Bank, Bajaj Finance, Asian Paints and SBI were among the laggards.
In the previous session, the BSE barometer settled 167.19 points or 0.56 per cent higher at 30,196.17, while the broader Nifty advanced 55.85 points or 0.63 per cent to end at 8,879.10.
Foreign portfolio investors offloaded equities worth Rs 1,328.31 crore in the capital market on Tuesday, provisional exchange data showed.
According to traders, stock-specific action led benchmarks higher in morning session.
Market bias remains negative along with continued volatility in the near term as the rising number of coronavirus cases in the country kept market participants on edge, they said.
The number of COVID-19 cases in India spiked to 1.06 lakh, while the death toll rose to 3,303, according to the health ministry.
Globally, the number of cases linked to the disease has crossed 48.97 lakh and the death toll has topped 3.23 lakh.
Bourses in Shanghai and Hong Kong were in the red, while Tokyo and Seoul were trading with gains.
Stock exchanges on Wall Street ended with losses in overnight session.
International oil benchmark Brent crude futures were trading 0.87 per cent higher at USD 34.95 per barrel. ANS DRR DRR