The domestic unit has risen by 22 paise against the dollar since Wednesday amid heightened global volatility.
Expectations of robust capital inflows into equities and debt largely supported the rupee gains.
It remained under immense pressure and drifted further to hit low of 64.4250.
However, it witnessed a remarkable turnaround in late afternoon deals and scaled fresh intra-day high of 64.2050 before settling at 64.21, showing a handsome gain of 12 paise, or 0.19 per cent.
Foreign investors continued to put money in stocks even as the benchmark BSE Sensex dropped by over 52 points. FPIs invested Rs 90 crore on net basis in stocks today, as per provisional exchange data.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.3554 and for the euro at 72.5092.
On the global front, the greenback edged higher against other major currencies. The dollar index, which tracks the US currency against a basket of six major rivals, was up 0.24 per cent at 96.89.
In cross-currency trades, the rupee weakened against the pound sterling to finish at 83.11 from 83.06 per pound, but held virtually steady against the euro at 72.15.
The domestic currency, however, firmed up further against the Japanese yen to conclude at 58.31 per 100 yens from 58.78 yesterday.
In forward market today, premium for dollar dropped on fresh receivings from exporters.
The benchmark six-month premium payable in November weakened to 138-140 paise from its previous level of 141-143 paise and far-forward May 2018 contract also slid to 284-286 paise from Wednesday's closing level of 289-291.
The oil price slipped below $50 a barrel despite a pledge by the world's largest exporters to extend an existing output cut.