After hitting a peak of 34,488.69, the 30-share index ended 284.01 points or 0.84 per cent higher at 34,109.54.
Similarly, the NSE Nifty jumped 82.45 points or 0.83 per cent to 10,061.55.
M&M was the top gainer in the Sensex pack, rising around 5 per cent, followed by Kotak Bank, Bajaj Finance, Nestle India, SBI, ICICI Bank, HDFC Bank and ONGC.
On the other hand, NTPC, IndusInd Bank, Bharti Airtel and Maruti were among the laggards.
The bulls maintained their grip on the market as stocks surged led by massive foreign fund inflows and positive global cues, analysts said.
On a net basis, foreign portfolio investors bought equities worth Rs 7,498.29 crore on Tuesday, provisional exchange data showed.
Further, gradual reopening of economies the world over has fuelled bullish trend in global markets, they said.
Bourses in Shanghai, Hong Kong, Tokyo and Seoul closed up to 2 per cent higher.
Exchanges in Europe were also trading on a positive note in early deals.
International oil benchmark Brent crude futures climbed 1.04 per cent to USD 39.98 per barrel.
On the currency front, the rupee surrendered all intra-day gains to provisionally settle 11 paise lower at 75.47 against the US dollar. ANS ABM ABM