After hitting a high of 30,847.10, the 30-share BSE barometer was trading 925.67 points or 3.10 per cent higher at 30,819.63.
Similarly, the NSE Nifty was quoting 270.05 points, or 3.09 per cent, up at 9,018.80.
HDFC was the top gainer in the Sensex pack, surging up to 5 per cent, followed by Maruti, Bharti Airtel, Bajaj Finance, Tata Steel, Hero MotoCorp and ICICI Bank.
On the other hand, HUL was the sole laggard.
In the previous session, the BSE barometer closed 173.25 points or 0.58 per cent lower at 29,893.96, and the Nifty settled 43.45 points, or 0.49 per cent, down at 8,748.75.
Foreign institutional investors (FIIs) were net buyers in the capital market, as they bought equity shares worth Rs 1,943.41 crore on Wednesday, according to provisional exchange data.
According to experts, hopes of another financial stimulus hope before the end of the lockdown period buoyed investor sentiment in early session.
Further, slowing pace of fresh COVID-19 cases has also lent some momentum to global markets, they said.
Bourses in Shanghai, Hong Kong, and Seoul were trading on a positive note, while those in Tokyo were in the red.
Benchmark exchanges on Wall Street ended significantly higher in overnight trade.
Brent crude futures, the global oil benchmark, rose 1.55 per cent to USD 33.34 per barrel.
The death toll due to the novel coronavirus in India rose to 166 and the number of cases to 5,734, according to the Union Health Ministry.
Global tally of the infections has crossed 14.8 lakh, with over 88,000 deaths.