The domestic currency largely withstood the mid-session discomfort in the midst of excess volatility and movements of the greenback in global trade.
This is the highest closing of the rupee since October 23, 2015, when it had closed at 64.83.
The overnight bullish dollar sentiment has been carried forward to the Asian session following impressive US economic news and expectations of tighter pace of monetary tightening by the Fed.
Fresh bout of dollar selling by exporters and persistent foreign capital inflows largely aided the recovery, a forex dealer said.
Meanwhile, domestic bourses succumbed to fag-end profit taking despite a strong start on investors caution amid soft Asian session, snapping a three-day spectacular rally driven by optimism surrounding the GST.
After a steady start at 64.92, the rupee bounced back and moved in a tight range of 64.79 and 64.9850 most part of the day with wide swings.
It finally ended the day at 64.85, revealing a smart gain of 7 paise, or 0.11 per cent at the Interbank Foreign Exchange (Forex) market.
Over the quarter, the home currency has strengthened by a whopping 307 paise or 4.52 per cent induced by a crucial victory for BJP in a key state election and big foreign inflows into markets.
In worldwide trade, the dollar index, which tracks the US currency against a basket of six major rivals, was down 0.11 per cent at 100.35.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.8386 and for the euro at 69.2476.
In cross-currency trade, the rupee also bounced back against the pound sterling to close at 80.93 from 81.00 per pound and continued to rule firm against the euro to finish at 69.31 compared to 69.75 earlier.
It also strengthened further against the Japanese Yen to settle at 58.01 per 100 yens from 58.44 yesterday.
On the equity front, the flagship Sensex retreated by 26.92 points to end at 29,620.50 after briefly reclaiming its previous record closing high, while broader Nifty ended flat at 9,173.75.
In the forward market, premium for dollar drifted further due to sustained receivings from exporters.
The benchmark six-month premium for August declined to 128-130 paise from 130.5-132.5 paise and the far-forward February 2018 contract also slipped to 279-281 paise from 284-286 paise on Thursday.
On the global commodity front, crude oil prices fell back from an overnight three-week high as cautious investors indulged in profit-booking at higher levels, though both US crude and international benchmark Brent traded well above the psychological USD 50/barrel mark.
PTI