The 30-share index was trading 101.08 points, or 0.28 per cent, higher at 36,775.60. The NSE Nifty was up 34.60 points, or 0.32 per cent, at 10,834.25.
IndusInd Bank was the top gainer in the Sensex pack, rallying around 4 per cent, followed by SBI, Tata Steel, Bajaj Auto, ITC, HDFC duo and Reliance Industries.
On the other hand, Infosys, HCL Tech, UltraTech Cement, Maruti and Axis Bank were among the laggards.
In the previous session, the BSE barometer ended 187.24 points or 0.51 per cent higher at 36,674.52; while the NSE Nifty settled with 36 points or 0.33 per cent gains at 10,799.65.
Foreign institutional investors were net buyers in the capital market on Tuesday, purchasing equities worth Rs 829.90 crore, provisional exchange data showed.
According to traders, stock-specific gains and sustained foreign fund inflow buoyed domestic investor sentiment.
However, weakness in global equities amid rising number of COVID-19 cases capped the gains, they said.
The number of cases around the world linked to the disease has crossed 1.17 crore and the death toll has topped 5.43 lakh.
In India, the number of infections spiked to 7.42 lakh and the death toll rose to 20,642.
Bourses in Shanghai and Hong Kong were trading with gains, while those in Tokyo and Seoul were in the red.
Stock exchanges on Wall Street ended on a negative note in overnight session.
Meanwhile, international oil benchmark Brent crude futures fell 0.16 per cent to USD 43.01 per barrel. ANS DRR DRR