Forex dealers said weakening of the US currency against the euro overseas and a recovery in local equities also favoured the rupee sentiment.
The local currency started the day at a firm note at 53.55 from yesterday's close of 53.77 against the dollar at the Interbank Foreign Exchange (Forex) market.
It moved in a range of 53.28-53.60 before settling for the day at 53.30, a gain of 47 paise, or 0.87 per cent.
Previously, rupee had ended at 52.87 on October 17, 2012.
"Rupee continued its upward movement today mainly buoyed by the rate cut by RBI, which has created some sense of optimism in the markets. Also, exporters are on a dollar selling spree as they are expecting this to be the peak for the local unit," IDBI Head (Treasury) N S Venkatesh said.
The rupee had gained 14 paise yesterday, after RBI cut its short-term lending (repo) rate and cash reserve ratio by 0.25 per cent, pumping in a liquidity of Rs 18,000 crore into the system.
Venkatesh said a recovery in local stocks and hopes of higher foreign fund inflows also aided the rupee, adding that it will strengthen to 52-level against dollar by March-end.
The dollar index was down by 0.24 per cent against a basket of six major currencies ahead of the policy announcement from US Federal and US growth data.
"Euro strengthening to 1.35-1.44 also worked in rupee's favour," Venkatesh said.
Foreign institutional investors today pumped in over USD 170 million (Rs 906.36 crore) into local equities today, according to provisional BSE data.
Meanwhile, the BSE benchmark Sensex closed marginally higher at 20,005. Pramit Brahmbhatt, CEO, Alpari Financial Services (India), said, "The rupee hit a 13-week high tracking gains in euro and other highly traded currencies against the US dollar".
The premium for the forward dollar fell back slightly on fresh stray recevings by exporters.
The benchmark six-month forward dollar premium payable in June ended down at 155-156-1/2 paise from Tuesday's close of 157-159 paise.
Far-forward contracts maturing in December finished a tad lower at 317-319 paise from 317-1/2-319-1/2 paise.
The RBI has fixed the reference rate for the US dollar at 53.5678 and for euro at 72.2340.
The rupee improved further against the pound sterling to 84.04 from previous close of 84.58 and also shot up against the Japanese yen to 58.41 per 100 yen from 59.48.
It, however, turned negative to close at 72.26 per euro from last close of 72.21.