The Tour entered the Pyrenees mountains for the first of three stages on Tuesday as the race builds towards its conclusion.
And it was Australian Rogers (Tinkoff-Saxo) that emerged victorious from a stage that featured five climbs, including one hors categorie ascent on the 237.5kilometre ride from Carcassonne to Bagneres-de-Luchon.
The 34-year-old finished nine seconds ahead of Europcar's Thomas Voeckler in second, with Vasil Kiryienka of Team Sky rounding off the top three.
Yellow jersey holder Vincenzo Nibali was over eight minutes behind Rogers, but he retains his lead of four minutes and 37 seconds over nearest challenger Alejandro Valverde.
Rogers was part of a three-man group that was first to reach the summit of the final 11.7km climb at Port de Bales.
Voeckler and Jose Serpa made it to the top ahead of Rogers, but the trio were soon joined by Kiryienka and Rogers' team-mate Cyril Gautier on the descent.
The presence of Gautier proved pivotal in deciding the outcome of the stage as Rogers was able to streak clear with 4.5km to go after the Frenchman had attempted a similar attack.
Astana rider Nibali may have retained his comfortable advantage, but it was a day of change in the general classification as Romain Bardet (AG2R La Mondiale) slipped to fourth.
Bardet lost almost two minutes on Nibali, Valverde and Thibaut Pinot (FDJ), who leapfrogged him into third and also snatched the young rider jersey from his French compatriot.
American Tejay van Garderen fell from fifth to sixth after dropping close to four minutes on the yellow jersey group, and is now four minutes and 19 seconds off third.
Meanwhile, there was more good news for Tinkoff Saxo as Rafal Majka took over the King of the Mountains jersey from Katusha's Joaquim Rodriguez by winning the sprint at the top of the Cote de Fanjeaux.