Dealers said the strength in the rupee was also supported by increased selling of the greenback by exporters and banks.
Globally, dollar and yen gained on Brexit-induced safe-haven buying.
The British pound crashed more than 1.5 per cent after four UK ministers resigned over Prime Minister Theresa May's Brexit deal. The euro, however, climbed to a two-week high.
It touched a low of 72.18, before finally finishing at 71.97, up by 34 paise.
The last time rupee breached the 72-level was on September 14, when it had closed at 71.84.
The rupee had gained 36 paise to end at 72.31 against the US dollar Wednesday. The local unit has now gained 92 paise, or 1.27 per cent, in three sessions.
"Drop in US 10-yr bond yield followed by gradual pick up in FII inflow to domestic market and slide in oil prices eased the concerns of liquidity," said Vinod Nair, Head of Research, Geojit Financial Services.
Brent crude, the international oil benchmark, was trading marginally higher at $66.63 per barrel.
Meanwhile, foreign institutional investors (FIIs) bought shares worth a net Rs 20.4306 billion Thursday, as per provisional data.
The BSE benchmark Sensex ended 119 points higher at 35,260.54 while the broader Nifty went past the 10,600 mark on positive investor sentiment.