Dollar-selling by exporters and expectations of more RBI measures strengthened the beleaguered rupee, adding to the broad market rally.
The Sensex closed 0.67 per cent, or 124.46 points, higher at 18,789.34.
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The Nifty ended 0.84 per cent, or 46.55 points, higher at 5,565.65.
The Nifty has lost 7.3 per cent since the RBI first announced the liquidity draining measures on July 15.
Stocks have fallen in 10 of the last 12 trading sessions, as investors turn wary of slowing growth and the weakening rupee, which tumbled to a record low on Tuesday despite the central bank's cash-draining measures.
"It's been a tough few weeks to be managing Indian and emerging Asian equities, and sentiment towards India is pretty much at rock bottom at the moment," said Jonathan Schiessl, investment manager of Ashburton Global Funds Chindia Equity Fund.
Shares in Ranbaxy Laboratories (RANB.NS: Quote, Profile, Research), India's top drugmaker by sales, zoomed over 30 percent on Thursday after it clocked better-than-expected sales in its key U.S. market.
The results were a relief after its shares had tumbled 36 percent as of Wednesday's close since the drug maker pleaded guilty to U.S. felony charges related to drug safety and agreed to pay $500 million in settlement
Shares in India's top car maker Maruti Suzuki (MRTI.NS: Quote, Profile, Research) ended 4.07 percent higher after the central bank removed restrictions on shareholding of foreign institutional investors.
Midcap stocks, which have faced the brunt of the recent selloff in equities, also staged a comeback with auto ancillary firm Bharat Forge(BFRG.NS: Quote, Profile, Research) jumping 16.93 percent.
The NSE Midcap index, which has lost 15 percent since the beginning of June, ended 1.24 percent higher.
However, drugmaker Lupin added to Wednesday's falls, slipping another 3.25 percent to end at 801.35 rupees, while Sun Pharmaceutical Industries Ltd (SUN.NS: Quote, Profile, Research) dropped 3.13 percent after unit Taro Pharmaceutical Industries Ltd (TARO.N: Quote, Profile, Research) reported a lower net profit.