Covering-up of short positions by speculators gave gains a push, traders said.
In a session marked by volatility, the 30-share Sensex settled 104.37 points, or 0.41 per cent, higher at 25,864.47.
The gauge had gained 149.57 points on Monday.
The broad-based NSE Nifty closed at 7,837.55, up 30.95 points, or 0.40 per cent. Intra-day, it traded between 7,860.45 and 7,793.
Improving macro parameters, including a narrowing trade deficit, came as another positive.
Sentiment, however, was broadly cautious in the wake of lacklustre September quarter earnings by several blue-chip companies while foreign institutional investors (FIIs) have remained net sellers so far this month.
"Rise in crude prices fuelled by geo-political tension has lifted sentiment globally. Finance minister's assurance of achieving fiscal deficit target of 3.9 percent of gross domestic product for the current fiscal bolstered confidence of investors," said Gaurav Jain, Director, Hem Securities.
The country's biggest private lender, ICICI Bank, ended 0.06 per cent higher after the company said it will sell 6 per cent stake in its life insurance arm, ICICI Prudential Life, for Rs 1,950 crore.
Vedanta Ltd, Tata Steel, Hindalco, HDFC and Sun Pharma too backed up up gains.
Among the 30-Sensex constituents, 20 stocks climbed while 10 led by Infosys and Dr Reddy's fell.
Sector-wise, BSE FMCG led the pack, up 2.17 per cent, followed by metal (1.03 per cent) and healthcare (0.79 per cent).
crore yesterday, according to provisional data.
Key indices in Hong Kong, Japan, Singapore, South Korea and Taiwan rose up to 1.50 per cent while China's Shanghai Composite retreated 0.06 per cent.
Europe was trading higher in the afternoon trade.
"On the micro front, investors are keenly waiting for the recommendations from the Seventh Pay Commission, which can revive the consumption growth of the economy and is positive for FMCG and consumer durables," said Vinod Nair, Head, Fundamental Research, Geojit BNP Paribas Financial Services.
The market breadth remained positive as 1,400 stocks ended higher, 1,288 finished in the red while 171 ruled steady.
Pramit Brahmbhatt, Veracity Group CEO, said, "Value-buying in the market helped indices rise more than over a quarter per cent during the day. The positive Asian markets supported the gains. Now, investors are waiting for the data due for the week.
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