After touching a high of 36,110.21, the 30-share index was trading 204.90 points, or 0.57 per cent, higher at 36,048.60, while the NSE Nifty rose 75.80 points, or 0.72 per cent, to 10,627.50.
Bajaj Auto was the top gainer in the Sensex pack, advancing around 2 per cent, followed by Asian Paints, Bharti Airtel, HUL, Reliance Industries, HUL and Kotak Bank.
On the other hand, Tata Steel, HDFC, M&M and Bajaj Finance were among the laggards.
In the previous session, the BSE barometer settled 429.25 points, or 1.21 per cent, higher at 35,843.70, and the broader Nifty surged 121.65 points, or 1.17 per cent, to close at 10,551.70.
Foreign institutional investors were net sellers on Thursday, offloading equities worth Rs 556.72 crore, provisional exchange data showed.
According to traders, domestic indices tracked gains in global benchmarks, which advanced after positive jobs data in the US enthused investors.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul were trading with gains.
Stock exchanges on Wall Street too ended on a positive note in overnight session following a record increase in payrolls and a decline in unemployment.
The gains were, however, capped as rising coronavirus cases across the world weighed on market mood, traders said.
The number of cases around the world linked to the disease has crossed 1.08 crore and the death toll has topped 5.20 lakh.
In India, the number of infections spiked to 6.25 lakh and the death toll rose to 18,213.
Meanwhile, international oil benchmark Brent crude futures fell 0.70 per cent to USD 42.84 per barrel. ANS DRR DRR