The gains were helped by a recovery in emerging markets following signs that Russia may be seeking to avoid further escalation of its military involvement in Ukraine, although gains in India far outperformed the region.
India is the second equity market after Indonesia, among the "Fragile Five" economies seen vulnerable to the U.S. Federal Reserve's stimulus tapering, that has turned positive for 2014, as a more stable currency and a sharply narrower current account deficit has attracted foreign flows.
Overseas investors bought Indian shares worth Rs. 198 crore on Monday, extending their buying streak to the twelfth day for a total of $765 million.
The BSE Sensex 1.26 per cent, or 263.08 points, to end at 21,209.73, its biggest daily percentage gain since January 13, and well beyond the 0.15 per cent gain in the MSCI Asia-Pacific index excluding Japan.
The BSE is now up 0.2 per cent for the year, having recovered since last month from its 3.1 per cent fall in January.
Nifty rose 1.23 per cent, or 76.50 points, to end at 6,297.95 on Tuesday, just 6 points away from turning positive for 2014, also marking its biggest single-day gain since January 15.
Bank stocks surged 2.6 per cent, their biggest single-day gain since December 9, 2013.Axis Bank rose 3 per cent, while ICICI Bank surged 3.8 per cent.
Among other stocks, Reliance Industries rose 1.2 per cent, while Larsen and Toubro gained 1.7 per cent.Bharat Heavy Electricals rose 2.6 per cent after Life Insurance Corporation of India on Monday bought a 4.66 per cent stake in it from the government of India in a block deal totalling Rs. 1,889 crore.
Dhanlaxmi Bank jumped 15.5 per cent after the small lender said it would issue 59.7 million shares on a preferential basis to investors it did not identify, for Rs. 39 each.
However, among stocks that fell, Dr Reddy's Laboratories ended 0.5 percent down, on concerns that sales in Russia and Ukraine would be hit, given military tensions between the two countries.
Dr. Reddy's has the highest exposure to Russia and the former Soviet republics, with the region accounting for 14.5 per cent of sales, Bank of America-Merrill Lynch said in a note.