Great Dane Rasmussen wearing yellow
The Rabobank rider finished two minutes and 47 seconds in front of Spanish pair Iban Mayo and Alejandro Valverde.
Mayo came in second and Valverde third after the 165km journey from Le Grand-Bornand to Tignes.
Rasmussen is top of the overall standings with a 43-second lead on German Linus Gerdermann and a two minutes 39 seconds advantage on Mayo in third place.
The 33-year-old moved in front after the descent at Cormet de Roseland with an aggressive break and was rarely threatened by the chasing pack over the remaining 64km.
Rasmussen’s last victory in the Tour came at stage 16 in 2006 from Bourg d’Oisans to La Toussuire.
Earlier, the first attack of the day had come from FDJ rider Lillian Jegou and he was joined by Gerolsteiner’s Stefan Schumacher.
German Schumacher collected three points from the first climb at Montee d’Hauteville.
T-Mobile’s riders maintained early control of the peloton as Schumacher continued ahead of the pack on the second climb at Col de Temie.
Schumacher took the points again on this climb ahead of Quick Step rider Juan Manuel Garate and Euskaltel’s Gorka Verdugo.
On the descent, it was Thomas Voeckler (Bouygues Telecom) who attacked and a group of 16 followed as Voeckler picked up the points on the third climb after 46km.
Australian Michael Rogers, who began the day in 14th place overall, moved into the escaping pack and seemed to emerge as the main threat to T-Mobile team-mate Gerdemann in the yellow jersey.
Rabobank’s Rasmussen led the chase to Rogers’ group and edged into the lead during the descent of the 19.9km-long third climb on the 1,967m-high Cormet de Roseland.
On the descent, Rogers crashed with Caisse d’Epargne rider David Arroyo and despite initially remounting with shoulder and knee injuries, the 27-year-old was caught by the peloton and decided to abandon the race with 30km remaining.
The descent also spelled the end of Stuart O’Grady’s 11th Tour after a crash in which he suffered back injuries, resulting in the winner of the Paris-Roubaix stage being taken to hospital.
Meanwhile, Rasmussen continued to extend his lead and collected the points at the top of the Montee d’Hautville.
With 25km remaining, he was six minutes ahead of the peloton.
With 10km left, the Dane was still in control with the chasing pack of Christophe Moreau, Cadel Evans, Alberto Contador, Frank Schleck, Andrey Kashechkin and Mayo all attempting attacks but largely remaining together.
The Dane remained relatively untroubled over the final five kilometres as the chasing pack seemed to accept his dominance of the race.
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