Heavy unwinding of dollars by some foreign banks and corporates predominantly supported the upbeat trend.
The rupee has appreciated by a whopping 39 paise in the last three days.
Expectations of encouraging GDP numbers after a dismal Q1 show are keeping the forex sentiment highly buoyant, a forex dealer said.
The GDP numbers for the September quarter will be released on Thursday.
The rupee resumed on a weak note at 64.46 at the Interbank Foreign Exchange (forex) market from Tuesday's close of 64.41 due to increased month-end dollar demand from importers and lost further ground to hit an intra-day low of 64.52.
However, overcoming early volatility, the domestic unit bounced back sharply to touch a high of 64.27 late afternoon deals before ending at 64.31, revealing a gain of 10 paise, or 0.16 per cent.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.4058 and for the euro at 76.3209.
Meanwhile, crude prices remained under pressure on growing doubts that OPEC and Russia will agree on extending production cuts and also due to reports of an unexpected rise in US crude oil inventories.
OPEC will host a meeting in Vienna tomorrow, with representatives from 13 oil-rich nations.
Brent crude, the international benchmark, is trading lower at USD 62.94 a barrel in early Asian trade.
Meanwhile, equity markets gave back all of its initial gains and ended marginally lower in a highly volatile trade on the back of profit-taking amid caution ahead of the expiry of November derivatives and release of Q2 GDP data on Thursday.
Asian bourses, however, closed higher as investors mostly shrugged off North Korea's latest missile launch.
On the global front, the dollar dipped against a basket of currencies, pulled down by broad strength in sterling as well as fresh tensions between the US and North Korea overshadowed the previous session's upbeat US data.
The dollar index, which measures the greenback's value against a basket of six major currencies, was up at 93.21 in early trade.
In cross-currency trades, the rupee fell back against the pound sterling to settle at 86.21 from 85.65 per pound, but remained firm against the Japanese yen to finish at 57.66 per 100 yens as compared to 57.87 yesterday.
The rupee also strengthened against the euro to close at 76.12 from to 76.57 earlier.
Elsewhere, the British pound traded broadly higher in Asia Pacific trade, building onto the overnight advance following reports that negotiators have reached a deal on the Brexit "divorce bill" that the UK will pay to meet its existing EU obligations before leaving the regional bloc.
The common currency euro is trading marginally up against the US dollar after a brief correction ahead of German inflation data.
In forward market today, premium for dollar continued its slide due to persistent receiving from exporters.
The benchmark six-month premium payable in April softened to 112-114 paise from 113-115 paise previously, while the far forward October 2018 contract ended steady at 254-256 paise.