Hunter covered the 114-mile course from Marseille to Montpellier in 3 hours, 47 minutes and 50 seconds and was first in a group of 10 riders who were all credited with the same time. It marked the 30-year-old Hunter's first stage win at the tour.
Fabian Cancellara, who was the overall leader in the early stages after taking the tour prologue, was second Thursday and Murilo Antoniobil Fischer third in the stage.
Rasmussen ended the stage in 46th place but just 7 seconds back of Hunter. Alejandro Valverde remained 2 minutes, 35 seconds behind Rasmussen in the overall standings and Iban Mayo is third, 4 seconds behind Valverde.
The tour's 12th stage is set for Friday and sends the racers on an 111.5-mile ride from Montpellier to Castres. The 20th and final stage of this year's Tour de France is scheduled for July 29, ending in Paris.