The Sensex rallied 246 points to reclaim the 35,000-mark in the the special Muhurat session on Wednesday to mark the beginning of Hindu Samvat year 2075.
After rising by 310 points in opening trade, the Sensex closed at 35,237.68, up 245.77 points, or 0.70 per cent.
All the sectoral indices were in the green, led by oil and gas, auto, realty and FMCG.
The broader NSE Nifty also rose by 68.40 points to 10,598.40, up 0.65 per cent.
The BSE Sensex gained 2,407.56 points, or 7 per cent, in the Samvat year 2074, while the Nifty rose by 319.15 points, or over 3 per cent.
Brokers said buying activity gathered momentum as investors opened their books on the first session of Samvat 2075.
Gaurav Ratnaparkhi, senior technical analyst, Sharekhan by BNP Paribas, said the “market momentum is expected to pick up on the upside once the Nifty crosses the range of 10,600-10,710. Once the hurdle zone is surpassed then the Nifty can stretch towards 11,000-11,140 in the short-term."
Meanwhile, US stocks edged lower on Thursday, as a clutch of weak earnings reports punctured a rally from the previous session, which was spurred by the outcome for midterm elections.
Stocks had gained more than 2 percent on Wednesday after Americans voted for a divided Congress, which was largely anticipated by investors who raised bets that it would be positive for stocks.
While it could make it harder for President Donald Trump to push through new legislations such as additional tax cuts, investors are hoping for compromise on policies such as increasing infrastructure spending.
Despite the dip in markets on Thursday, traders said investors were largely positive about the election outcome.
The Fed, which is set to release its rate decision at 2:00 pm ET, is expected to leave interest rates unchanged, but the statement that follows could lay the ground for a fourth rate hike in December and for the next year.
European shares hit a one-month high after Asia and Wall Street had set similar milestones overnight.
Oil prices were subdued after data showing a surge in US energy stockpiles, although there was some support from reports Opec may reduce output next year.