The Nifty also bounced back, rising 97.6 points to hit its fresh all-time high of 23,966.40.
Benchmark indices rebounded after falling in early trade on Thursday, with the Sensex breaching the historic 79,000-mark for the first time and the Nifty hitting its fresh record high, amid buying in blue-chip stocks.
The 30-share BSE Sensex jumped 339.51 points to hit its new lifetime peak of 79,013.76 after falling in early trade, helped by buying in blue-chips Reliance Industries and ICICI Bank.
The Nifty also bounced back, rising 97.6 points to hit its fresh all-time high of 23,966.40.
Among the 30 Sensex companies, UltraTech Cement, JSW Steel, Reliance Industries, Axis Bank, ICICI Bank, Bajaj Finance, Kotak Mahindra Bank and Tata Steel were the biggest gainers.
Maruti, Tech Mahindra, HCL Technologies and Larsen & Toubro were the biggest laggards.
"The market will remain bullish in the near-term despite the valuation concerns, and the ongoing momentum has the potential to take the Sensex to 80,000 levels.
"A healthy trend in the market is that now the up move is being led by fundamentally strong largecaps in sectors like banking and telecom. With RIL, which had not participated in the rally till yesterday joining the bull bandwagon, the rally has the strength to continue," said V K Vijayakumar, Chief Investment Strategist, Geojit Financial Services.
In Asian markets, Seoul, Tokyo, Shanghai and Hong Kong were trading lower.
US markets ended in positive territory on Wednesday.
Foreign Institutional Investors (FIIs) offloaded equities worth Rs 3,535.43 crore on Wednesday, according to exchange data.
Global oil benchmark Brent crude declined 0.21 per cent to USD 85.07 a barrel.
The BSE benchmark Sensex climbed 620.73 points or 0.80 per cent to settle at a new closing peak of 78,674.25 on Wednesday.
The Nifty went up by 147.50 points or 0.62 per cent to settle at a record closing peak of 23,868.80.
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)