The close was also a two-week high for the market.
The NSE Nifty too retook the 7,800-level. The rally came on the back of a flurry of buying activity and a firm overseas trend after the US Federal Reserve hiked rates for the first time in nearly a decade.
At 66.42, the rupee closed on a firm note against the dollar, which kept the mood upbeat.
In its longest winning-run this month so far, the BSE Sensex took off on a positive note before settling higher by 309.41 points, or 1.21 per cent at 25,803.78.
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Intra-day, it slipped into the negative zone briefly as participants locked in gains amid lingering uncertainty over passage of the key GST Bill. The gauge had gained about 450 points in the previous three sessions.
The 50-share NSE Nifty recaptured the 7,800-mark by surging 93.45 points, or 1.21 per cent, at 7,844.35.
"Equity benchmarks rallied on dovish comments from Fed chief Janet Yellen post a rate hike... Further, appreciation of the rupee against the dollar, lower level buying and short covering also helped the indices," said Gaurav Jain, Director, Hem Securities.
Tata Steel was the best performer on the BSE Sensex, up 4.76 per cent, as Vedanta Ltd and Hindalco too gained.
Out of the 30-share Sensex pack, 25 ended higher.
Meanwhile, Fitch Ratings said India is not immune to potential market jitters following interest rate hike by the US Fed, but favourable growth outlook makes it attractive for foreign investors.
Sector-wise, the BSE metal index gained the most by surging 2.46 per cent, followed by power 1.44 per cent, healthcare 1.39 per cent and auto 1.33 per cent.
The small-cap index rose 1.72 per cent and mid-cap 1.56 per cent.
"The Fed has also signalled that any future rate hike will
be gradual, which is certainly positive for EMs like India. Market would now shift its focus back to domestic factors like the ongoing winter session of Parliament," said Vinod Nair, Head-Fundamental Research, Geojit BNP Paribas Financial Services Ltd.
Key indices in China, Hong Kong, Japan, Singapore, South Korea and Taiwan rose by up to 1.81 per cent.
A similar effect was visible in Europe, which was trading higher in early trade.
The market breadth remained negative as 1,946 stocks ended lower, 743 closed higher while 212 ruled steady.
The total turnover went up to Rs 3,149.45 crore from Rs 2,722.72 crore yesterday.