After hitting a high of 33,640.73, the 30-share index was trading 895.69 points or 2.74 per cent higher at 33,615.85.
Similarly, the NSE Nifty shot up 247.20 points, or 2.59 per cent, to 9,800.55.
Maruti was the top gainer in the Sensex pack, rallying nearly 7 per cent, followed by M&M, ICICI Bank, Infosys, Tata Steel, Bajaj Auto, Axis Bank and Bajaj Finance.
Shares of Reliance Industries, HUL and Tech Mahindra were trading on a positive note ahead of their earnings announcements.
On the other hand, Sun Pharma was the sole laggard.
In the previous session, the BSE barometer settled 605.64 points or 1.89 per cent higher at 32,720.16, while the Nifty advanced 172.45 points, or 1.84 per cent, to close at 9,553.35.
Foreign portfolio investors turned net buyers in the capital market on Wednesday, as they purchased equity shares worth Rs 722.08 crore, according to provisional exchange data.
Investor sentiment improved on hopes that gradual lifting of global lockdowns would help start economic recovery, they added.
Investor sentiment was buoyed by news of a possible breakthrough in testing for a treatment of COVID-19.
Top US epidemiologist Anthony Fauci said that Gilead Science's remdesivir "has a clear-cut, significant, positive effect in diminishing the time to recovery".
Further, the US Federal Reserve signalled on Wednesday that it will keep its key short-term interest rate near zero for the foreseeable future as part of its extraordinary efforts to bolster the economy.
Bourses in Shanghai and Tokyo were trading with significant gains, while those in Hong Kong and Seoul were closed for a holiday.
On Wall Street, key indices ended with massive gains in overnight trade.
International oil benchmark Brent crude futures rallied 9.57 per cent to USD 26.55 per barrel.
Meanwhile, global tally of coronavirus infections was over 31.93 lakh, with around 2.27 lakh deaths.
The death toll due to COVID-19 in India rose to 1,074 and the number of cases climbed to 33,050 in the country, according to the Union health ministry. ANS DRRDRR