Armstrong, who is going for his seventh straight Tour victory, picked up more than a minute on second-place rider Mickael Rasmussen of Denmark, the New York Times reported. He finished second in the race's 14th stage, 56 seconds behind Georg Totschnig of Austria.
The stage was conducted over 137 miles of a mountain course with temperatures reaching 108.
"A very tough day with the heat and the distance," said Armstrong. "If it's this hot again tomorrow, a lot of riders will be going home."
Armstrong is now 1 minute 41 seconds ahead of Rasmussen.