Alberto Contador, continuing a furious attempt to close the General Classification gap with Froome, had an 11-second advantage on Froome at the day's second checkpoint.
But just before that spot 12.4 miles from the finish, Froome opted to change to a more aerodynamic bike, a decision that may have been the difference in the stage.
Froome covered the final leg of the stage in 12 minutes, 58 seconds, quick enough to end up 9 seconds better than Contador.
Froome extended his overall lead to 4:34 over Contador, who moves into second place overall. Roman Kreuziger is third, 4:51 back of Froome, while Bauke Mollema, dropping from second to fourth, is 6:23 behind the leader.
Froome's total time for the 19.9-mile run Wednesday from Embrun to Chorges was 51:33. It was his third stage win of this year's Tour de France and keeps him in the leader's yellow jersey for a 10th consecutive stage.
Joaquin Rodriguez was third in the stage, 10 seconds back of Froome. Kreuziger came in fourth another 13 seconds off the pace while Alberto Valverde, who put up a strong early time, was fifth, 30 seconds behind Froome's time.
The riders have a 107.2-mile challenge ahead of them Thursday with a route from Gap to Alpe-d'Huez that includes a Category 3 and two Category 2 climbs along with two climbs rated beyond categorization.