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.
At the interbank forex market, the rupee opened firm at 72.04 and rose further to 71.87 per US dollar.
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 USD 66.63 per barrel.
Meanwhile, foreign institutional investors (FIIs) bought shares worth a net Rs 2,043.06 crore 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.