The Sensex finished above the psychologically key 60,000-mark while the Nifty surged past the 18,000-level on Monday on across-the-board buying amid a mixed trend overseas.
A depreciating rupee and concerns over the US Federal Reserve hiking rates later this week failed to quell investors' appetite for stocks, traders said.
The 30-share BSE Sensex rallied 786.74 points or 1.31 per cent to settle at 60,746.59.
During the day, it jumped 826.85 points or 1.37 per cent to 60,786.70.
On similar lines, the broader NSE Nifty advanced 225.40 points or 1.27 per cent to end at 18,012.20.
UltraTech Cement topped the Sensex gainers' chart with a jump of 4.18 per cent, followed by HDFC, Sun Pharma, M&M, HDFC Bank, Larsen & Toubro, Bajaj Finserv and Bajaj Finance.
Only three counters closed in the red -- Dr Reddy's, NTPC and IndusInd Bank, slipping up to 0.66 per cent.
"Investors are hoping for a smaller rate hike by the US Federal Reserve this week against the earlier expectation of a more aggressive rate increase.
"This optimism has fuelled a sharp upsurge, which has pushed both the local benchmark indices above their key psychological levels.
"Also, FIIs are looking at local shares with renewed interest, which has boosted the investors' sentiment.
"However, if the Fed adopts any hawkish stance, markets could be in for a steep correction in the near term," said Shrikant Chouhan, Head of Equity Research (Retail), Kotak Securities Ltd.
Vinod Nair, head of research at Geojit Financial Services, said the buoyancy of Wall Street was reflected well in the domestic market, supported by sliding oil prices following weak Chinese factory data.
"US stocks recovered from a tech sell-off on hopes that the Fed would hint towards dialling down big interest rate hikes," he noted.
In the broader market, the BSE midcap gauge jumped 1.24 per cent and the smallcap index climbed 0.45 per cent.
All BSE sectoral indices ended higher, with auto advancing 1.57 per cent, followed by teck (1.45 per cent), industrials (1.43 per cent), consumer discretionary (1.37 per cent), telecommunication (1.35 per cent) and commodities (1.12 per cent).
World stocks were mixed ahead of the Fed's monetary policy decision on Wednesday amid indications of another rate hike to tame runaway inflation.
Elsewhere in Asia, markets in Seoul and Tokyo ended higher, while Shanghai and Hong Kong settled in the red.
Stock exchanges in Europe were trading on a mixed note in mid-session deals.
Wall Street had ended significantly higher on Friday.
International oil benchmark Brent crude was trading 0.31 per cent lower at $95.47 per barrel.
Foreign Institutional Investors (FIIs) were buyers on Friday as they bought shares worth a net Rs 1,568.75 crore, as per exchange data.
