The broader index Nifty also climbed 168.50 points, or 0.81 per cent to hit its lifetime high of 20,855.30 with 32 of its components closing in the green.
The market capitalisation of BSE-listed firms surged by more than Rs 2.5 lakh crore to cross Rs 350 lakh crore on Tuesday.
Analysts said the positive sentiment was fuelled by unabated inflow of foreign funds on the back of robust sentiment built up over favourable macroeconomic data in the previous week and the results of assembly polls of Madhya Pradesh, Rajasthan and Chhattisgarh that raised expectations of longer political stability in the country.
Also, investors are expecting the Reserve Bank to maintain the status quo on the interest rate in its bi-monthly monetary policy decision to be announced on Friday, they said.
Among major Sensex movers, Power Grid rose the most by 4.46 per cent, NTPC by 3.89 per cent, SBI by 2.31 per cent and ICICI Bank by 2.28 per cent. Other gainers included Mahindra & Mahindra, Titan and Maruti.
On the other hand, Hindustan Unilever, HCL Tech, Bajaj Finance remained laggards with losses of up to 1.49 per cent.
Foreign institutional investors purchased shares worth Rs 2,073.21 crore on Monday, according to exchange data.
"The domestic market extended the gains and hit fresh highs despite cautiousness among global peers ahead of key US job data this week. The aura of the state election results and other positive factors like above-expected earnings and GDP growth data are supporting the return of FII flows to the Indian market," said Vinod Nair, Head of Research at Geojit Financial Services.
"The RBI's monetary policy meeting is expected to be status quo. However, the commentary on economic growth, foodgrain prices and inflation trajectory will be closely watched," he added.
The market rally was also fueled by gains in Adani group stocks which Adani soared up to 20 per cent following a report that the US agency found short-seller Hinderburg Research's allegations of corporate fraud against the conglomerate were not relevant.
Adani Energy Solutions and Adani Green Energy zoomed 20 per cent each to close at Rs 1,082.60 and Rs 1,348 apiece. Adani Total Gas surged 19.95 per cent to settle at Rs 878.20, and NDTV jumped 18.41 per cent to Rs 266.55.
In the broader market, the BSE largecap index surged 1.01 per cent, midcap gauge gained 0.14 per cent and smallcap advanced marginally by 0.12 per cent.
Among sectoral indices, utilities surged the highest 6.54 per cent followed by power rising by 6.09 per cent. While services index went up 3.93 per cent, commodities advanced 2.04 per cent and oil & gas jumped 1.84 per cent. Bankex rose 1.21 per cent and energy inched up by 1.17 per cent.
Realty index declined by 0.65 per cent, while IT and teck slipped by 0.57 per cent and 0.43 per cent, respectively. Telecommunications, healthcare and FMCG were other laggards.
On the domestic macroeconomic front, the services sector growth in India fell to a one-year low in November on softer expansions in new work intakes and output, despite receding price pressures, a monthly survey said on Tuesday.
The seasonally adjusted S&P Global India Services Business Activity Index fell from 58.4 in October to a one-year low of 56.9 in November.
In Asian markets, Hang Seng and Nikkei 225 traded lower by 2.07 per cent and 1.37 per cent, respectively, while China's Shanghai Composite declined 1.67 per cent.
European markets were mixed. Germany's DAX gained 1.51 per cent and France's CAC 40 by 0.69 per cent. London's FTSE 100 declined 0.22 per cent.
The US markets ended on a mixed note with S&P 500 registering a loss of 0.54 per cent on Monday.
Meanwhile, global oil benchmark Brent crude advanced 1 per cent to USD 78.81 a barrel.
On Monday, the 30-share BSE Sensex jumped 1,383.93 points, or 2.05 per cent, to close at a lifetime high of 68,865.12. The barometer logged its biggest single-day jump since May 20, 2022. Nifty also climbed 418.90 points, or 2.07 per cent, to hit 20,686.80.