Weakness of the American currency in the overseas market also helped the domestic unit, forex dealers said.
However, higher crude prices restrained the rupee to gain momentum, they added.
At the interbank foreign exchange, the domestic unit opened strong at 75.27 against the US dollar, then gained further ground to 75.25, registering a rise of 12 paise against the previous close.
In initial deals, the rupee was trading in a tight range of 75.25 and 75.27 with a positive bias against the greenback.
The domestic had settled at 75.37 against the US currency on Wednesday.
On the domestic equity market front, the BSE Sensex was trading 327.18 points or 0.54 per cent higher at 61,064.23, while the broader NSE Nifty surged 114.05 points or 0.63 per cent to 18,275.80.
Foreign institutional investors emerged as net buyers in the capital market on Wednesday, as they purchased shares worth Rs 937.31 crore, as per exchange data.
Meanwhile, the dollar index, which gauges the greenback''s strength against a basket of six currencies, slipped 0.03 per cent to 94.05.
Global oil benchmark Brent crude futures rose 0.70 per cent to USD 83.76 per barrel.