After hitting a high of 31,660.60 during the day, the 30-share index settled 995.92 points or 3.25 per cent higher at 31,605.22.
Similarly, the broader NSE Nifty surged 285.90 points or 3.17 per cent to 9,314.95.
Axis Bank was the top gainer in the Sensex pack, soaring over 13 per cent, followed by ICICI Bank, HDFC Bank, IndusInd Bank and Bajaj Finance.
On the other hand, Sun Pharma, UltraTech Cement, Titan and Asian Paints were among the laggards.
Despite concerns over COVID-19, market participants preferred to accumulate stocks ahead of the expiry of May futures and options contracts, propelling benchmark indices, experts said.
Further, positive cues from most global markets and strong foreign fund inflows also enthused domestic investors, they said. Foreign portfolio investors purchased equities worth a net Rs 4,716.13 crore on Tuesday, provisional exchange data showed.
Bourses in Tokyo and Seoul ended with gains, while Shanghai and Hong Kong closed in the red.
Stock exchanges in Europe were trading with significant gains in early deals.
International oil benchmark Brent crude futures slipped 0.91 per cent to USD 35.84 per barrel.
On the currency front, the rupee depreciated 5 paise to provisionally settle at 75.71 against the US dollar.
Meanwhile, the number of coronavirus cases in India climbed to 1,51,767 and the death toll touched 4,337, as per health ministry data.
Globally, the number of cases linked to the disease has crossed 55.89 lakh, with the death tally at around 3.50 lakh. ANS ABM ABM