The Sensex started to capitalise on earlier gains by jumping 81 points to 31,393 on Tuesday as rising Asian shares kept the pitch conducive to buy more.
An upbeat assessment of the US economy by a top Federal Reserve official took Wall Street to a record close, which had a rub-off on Asia.
The 30-share BSE index rose 80.96 points, or 0.25 per cent to 31,392.53. It had gained 255.17 points in the previous session.
Also, the 50-share NSE Nifty moved to 9,674.80, up 17.25 points, or 0.17 per cent.
All sectoral indices saw buying interest, led by IT, technology, capital goods and auto stocks.
Prominent gainers were Tata Motors, Infosys, PowerGrid, Tata Steel, Reliance Industries and ONGC, rising by up to 1.45 per cent.
Japan's Nikkei was up 1.10 per cent while Hong Kong's Hang Seng index rose 0.40 per cent in morning trade. Shanghai composite inched up 0.04 per cent.
The US Dow Jones Industrial Average ended 0.68 per cent higher yesterday.