Fedrigo and Vande Velde pulled away from a lead group of six riders as the race entered its final mile. Fedrigo led the way to the final 200 yards and then watched for Vande Velde to make a move.
When Vande Velde did start a sprint, Fedrigo immediately took charge and pulled away for the win.
Fedrigo finished the 98.5-mile run from Samatan to Pau in southwestern France in 3 hours, 36 minutes, 34 seconds. Vande Velde was credited with the same time. Nick Sorensen and Thomas Voeckler were the next across, both timed at 16 seconds behind Fedrigo.
It was Fedrigo's fourth career stage victory. He also won the stage that ended in Pau in 2010.
Bradley Wiggins retained the overall lead, keeping 2 minutes, 5 seconds ahead of Christopher Froome. Vincenzo Nibali is third another 18 seconds back and defending Tour de France champion Cadel Evans is fourth, 3:19 back of Wiggins.
The Tour de France has an off day Tuesday before resuming Wednesday with a 122.4-mile route from Pau to Bagneres-de-Luchon through the Pyrenees. The race includes two Category 1 climbs near the end of the route after two climbs beyond categorization.