Rasmussen completed the 136.5-mile run from Orthez to Gourette-Col d'Aubisque in the Pyrenees in 6 hours, 23 minutes and 21 seconds, beating stage runner-up Levi Leipheimer by 26 seconds. Alberto Contador was third, 35 seconds behind Rasmussen.
It was Rasmussen's second stage victory this year and pushed his overall advantage to 3 minutes, 10 seconds over Contador. Cadel Evans struggled to keep up with the leaders in the final climb Wednesday and finished fourth.
Evans is more than 5 minutes behind Rasmussen in the overall standings.
Leipheimer is fourth overall, 5:59 off the pace.
Four stages remain in this year's Tour de France, including Thursday's 118-mile route from Pau to Castellsarrasin. The tour is to wrap up Sunday in Paris.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys