After hitting a high of 32,164.65, the 30-share index pared gains to trade 151.91 points or 0.48 per cent higher at 31,894.99.
Similarly, the NSE Nifty advanced 60.05 points, or 0.65 per cent, to 9,342.35.
IndusInd Bank was the top gainer in the Sensex pack, rallying over 8 per cent, followed by Axis Bank, HDFC, Tech Mahindra, ICICI Bank, Kotak Bank and SBI.
On the other hand, Sun Pharma, HCL Tech, Reliance Industries and Bharti Airtel were among the laggards.
In the previous session, the BSE barometer settled 415.86 points or 1.33 per cent higher at 31,743.08, while the Nifty closed 127.90 points, or 1.40 per cent, to 9,282.30.
Foreign portfolio investors were net sellers in the capital market on Monday, as they offloaded equity shares worth Rs 916.42 crore, according to provisional exchange data.
The Reserve Bank of India's Rs 50,000-crore liquidity booster to the mutual fund industry has spurred buying in financial stocks, traders said.
Expectation of another stimulus package by the government has also buoyed investor sentiment, they added.
However, weakness in other Asian markets and intensifying rout in US crude oil kept global market jittery.
Bourses in Shanghai and Hong Kong were trading on a positive note, while those in Tokyo and Seoul were in the red.
On Wall Street, key indices ended with significant gains in overnight trade.
International oil benchmark Brent crude futures fell 2.77 per cent to USD 22.43 per barrel.
West Texas Intermediate, the American benchmark, for June delivery dropped 14.8 per cent to USD 10.88 a barrel -- a day after plunging 25 per cent – as storage concerns mounted on weak demand amid coronavirus-led lockdowns.
Meanwhile, global tally of coronavirus infections has crossed 30 lakh, with over 2.11 lakh deaths.
Death toll in India rose to 934, while COVID-19 cases climbed to 29,435, as per health ministry data. ANS DRRDRR