Evans, who started the day fourth overall, struggled on the last two climbs, while Bradley Wiggins wore the yellow jersey a little more comfortably.
Voeckler dominated the 197-kilometre (123-mile) course from Pau to Bagneres-de-Luchon, the Frenchman leading a breakaway for his second stage victory of the Tour. He also won Stage 10.
Denmark's Chris Anker Sorensen was second, more than 1 1/2 minutes behind Voeckler. The top title contenders — Wiggins, his Sky teammate Christopher Froome of Britain, and Vincenzo Nibali of Italy — finished over 7 minutes back.
Overall, Wiggins leads second-placed Froome by 2:05, and third-placed Nibali by 2:23.
The Tour was riding under a new doping cloud after RadioShack team leader Frank Schleck was expelled from the race on Tuesday after testing positive for a banned diuretic.