It finally ended at 32,949.21, up 352.03 points, or 1.08 per cent - its biggest single-day gain since November 1, when it had surged 387.14 points.
The NSE Nifty too was quoting 28.30 points, or 0.27 per cent, down at 10,099.45.
Broader markets rallied with BSE Midcap index adding 231 points or 1.38 per cent to end at 16,893.61 and Smallcap index closing at 18,031.24, up 1.29 per cent or 230 points.
After a strong start at 32,968.02, the Sensex reclaimed the 33,000-mark to hit a high of 33,008.62 points but profit- booking at higher levels capped the gains.
Out of 1,989 stocks traded on the NSE, 1,219 advanced, 474 declined and 296 remained unchanged today.More news: Franken To Make Announcement Thursday, Senators Call For Resignation
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"Markets bounced back strongly on Thursday after the sell-off seen in the previous session".
The index had lost 205 points on Wednesday after the Reserve Bank held the policy rate and raised the inflation forecast for the remainder of the financial year. Most Asian shares declined as United States policy uncertainty kept sentiment in check.
Indian shares rose sharply on Thursday as firm global cues and a steep fall in oil prices overnight spurred investors to go bargain hunting after last week's heavy losses. Asian major also settled higher on Thursday with Nikkei 225 index climbing over 1 per cent followed by Hang Seng 0.28 per cent.