The 30-share barometer moved up by 50.17 points, or 0.17 per cent, at 29,094.61 with banking, power, FMCG, consumer durables, capital goods, realty, PSU and oil & gas sector stocks, leading the rise.
The gauge had gained 165.06 points in the previous session on Monday as stock markets remained closed yesterday on account of "Ambedkar Jayanti".
Similarly, the National Stock Exchange index Nifty rose by 10.80 points, or 0.12 per cent, at 8,844.80.
Besides, a slightly better trend at other Asian markets influenced trading sentiments here, they said.
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Meanwhile, Foreign Portfolio Investors (FPIs) bought shares worth Rs 417.01 crore on Monday, while Domestic Institutional Investors (DIIs) bought shares worth Rs 46.42 crore, as per provisional data available with stock exchanges.
Among other Asian markets, Hong Kong's Hang Seng was up by 0.08 per cent, while Japan's Nikkei gained 0.02 per cent in early trade.
The US Dow Jones Industrial Average ended 0.33 per cent higher in yesterday's trade.