This is its highest closing since August 11, 2015, when it had ended at 64.19 against the greenback.
Speculative traders and exporters offloaded their long dollar bets, spooked by launch of US air strikes against Syria.
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For the third straight day, the rupee has appreciated, in all by a whopping 75 paise against the dollar.
The domestic currency market remained largely buoyant.
Though domestic bourses succumbed to heavy profit-taking as investors sentiment turned sour reacting to the geopolitical developments after US attacks on a Syrian air base sent Asian markets lower.
A highly volatile dollar overseas along with uncertainties surrounding US President Donald Trump's fiscal policy helped the rupee close higher too.
The overall forex market sentiment also got a leg-up after the RBI projected India's growth at 7.4 per cent for the current fiscal, up from 6.7 per cent.
However, the apex bank kept its benchmark lending rate unchanged at 6.25 per cent for the third review in a row, citing upside risk to inflation.
The RBI, meanwhile, fixed the reference rate for the dollar at 64.3928 and for the euro at 68.5590.
In worldwide trade, the dollar traded little changed against the its major rivals ahead of key macro data, including the much-awaited US jobs numbers.
The dollar index, which tracks the US currency against a basket of six major rivals, was higher at 100.77.
Meanwhile, crude oil prices surged to a one-month high to trade above the USD 55-mark on growing worries about regional supply disruption while precious gold jumped to a high of USD 1,269.40 per ounce, setting a fresh high for the year.
In cross-currency trade, the rupee rallied against the pound sterling to close at 79.81 from 80.40 and hardened against the euro to finish at 68.33 compared to 68.86 earlier.
The local currency also firmed up against the Japanese yen to settle at 58.07 per 100 yens from 58.14 yesterday.
In the forward market today, premium for dollar maintained its strong upmove due to sustained paying pressure from corporates.
The benchmark six-month premium for September moved up to 157-159 paise from 156-158 paise and the far-forward March 2018 contract also edged up to 314-316 paise from 311-313 paise on Thursday.
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