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Heavy foreign funds inflows in fundamentally strong sectors such as property, banking, oil & gas and better than expected corporate earning trends helped the surge.
The benchmark index touched 21,039.42 before slipping back.
The last time the Sensex was above 21,000 was on November 8, 2010.
India was the best performing market in Asia on Thursday, with shares up 0.9 per cent at 05:50 GMT
The wide-based National Stock Exchange index Nifty rose by 67.40, or 1.09 per cent to 6,245.90 points.
Brokers said sentiments turned buoyant on heavy buying by foreign funds in blue-chip stocks available at attractive lower levels following two days of losses.
The Indian Central Bank will announce its policy review on October 29.