The Frenchman, fourth overall last year, took advantage of the four classic climbs on the 197km stage from Pau to drop the members of a 38-man breakaway one by one and bag the fourth Tour stage of his career.
The Aubisque, Tourmalet, Aspin and Peyresourde mountain passes were too much to handle for defending champion Cadel Evans, who lost ground on the last two climbs and crossed the finish line nearly 12 minutes behind Voeckler.
The Australian now lies eighth overall, 8:06 behind Bradley Wiggins, who firmly held on to his leader's yellow jersey.
""It's over for the Tour victory," said Evans's BMC team manager Jim Ochowicz.
Briton Wiggins was twice taunted by Italy's Vincenzo Nibali in the Peyresourde ascent but bridged the gap easily with the help of team mate Chris Froome.
The three rode the finale side by side and are likely to be the three riders on the final podium in Paris on Sunday.
Overall, Wiggins leads Froome by 2:05 while Nibali is still third, 2:23 behind.
Thursday's 143.5km 17th stage, finishing uphill in the ski resort of Peyragudes, will be the last chance for Wiggins's rivals to try to topple him.
Wednesday's stage started without Luxembourg's Frank Schleck, ruled out of the Tour by his RadioShack-Nissan team after failing a dope test for a diuretic.
