The 30-share index started the session on strong footing and hit the day's high of 24,709.09 points as stocks of capital goods, PSU, banking, oil and gas, power, metal and auto sectors rose sharply.
The Sensex settled at 24,684.85 points, a rise of 467.51 points, or 1.93 per cent, the biggest gain since May 12.
The broad-based Nifty of the National Stock Exchange also jumped by a whopping 132.55 points, or 1.83 per cent, to closed at 7,362.50 after testing a high of 7,368.60.
A firming trend in global markets also buoyed the sentiments, they added.
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Foreign institutional investors (FIIs) bought shares worth a net Rs 2,977.62 crore last Friday, as per provisional data from the stock exchanges.
Stocks of state-run banks led by SBI were in keen demand on speculation that the government may consider selling part of its holdings, attributed major support to the Sensex, brokers said.
SBI rose by 4.23 per cent while private lender Axis Bank jumped 3.59 per cent, HDFC Bank by 3.26 per cent and ICICI Bank by 2.80 per cent.
Car maker Maruti Suzuki surged 3.06 per cent after it reported 19.2 per cent rise in May sales.
The Mid-cap index gained by 2.16 per cent and small-cap index by 2.01 per cent. The BSE Capital goods index gained 4.93 per cent, followed by PSUs index (3.42 per cent), Banking index (3.28 per cent) and Oil and gas index (2.85 per cent).