This is the first time that the 30-stock Sensex has crossed the 80,000 mark.
The shares rose to record highs at the open on Wednesday, led by the country's top private lender HDFC Bank, which jumped to a record high on hopes of a likely increase in its weightage in a key global index.
The NSE Nifty 50 was up 0.7% at 24,291.75 points, while the S&P BSE Sensex added 0.72% to 80,013.77 points, as of 9:15 a.m. IST.
This is the first time that the 30-stock Sensex has crossed the 80,000 mark.
HDFC Bank rose 3.5% at the open, leading Nifty 50 gains.
"After the solid bull run in markets, now HDFC Bank is set to give another boost," said Abhilash Pagaria, head of Nuvama Alternative and Quantitative Research.
Foreign institutional investors' shareholding in HDFC Bank in the June quarter dropped below 55%, data released post market hours on Tuesday showed, raising the possibility of a likely increase in weightage in global index provider Morgan Stanley's MSCI indexes.
"A weight increase could bring in $3.2 billion-$4 billion inflows over six days," Nuvama's Pagaria said.
Inflows into HDFC Bank could further boost the benchmarks as it is the heaviest weighted stock in the Nifty and Sensex, according to analysts.
All 13 major sectors logged gains. The rise in HDFC Bank powered banks, financials and private banks 1.3%-1.5% higher.