Froome outpaced his British countryman as well as defending champion Cadel Evans down the stretch at La Planche des Belles Filles, France, taking the 124-mile Stage 7 with a time of 4 hours, 58 minutes and 35 seconds.
Evans claimed the runner-up spot 2 seconds behind Froome, just edging Wiggins, who nevertheless wrested the mantle of overall leader from the Australian with the performance.
The Briton established a 10-second advantage at the top of the board.
Finishing fourth another 5 seconds back was Italy's Vincenzo Nibali. He used the effort to secure third place overall, 16 seconds behind Wiggins.
The finish at La Planche des Belles Filles -- a new addition to the Tour de France -- includes a steep climb during the last few miles, with the final 100 meters at a 14-percent grade.
That climb took a toll on Switzerland's Fabian Cancellara, who lost the yellow jersey for the first time since the prologue. He finished 1:52 off Froome's pace for the day and fell to 11th overall.