Rasmussen has been King of the Mountains in the last two years
Denmark's Michael Rasmussen went it alone for victory in Tignes to secure the Tour de France yellow jersey.
Rasmussen, who began the day 39th overall, was part of a breakaway halfway through the 165km eighth stage.
He went solo on the last climb to finish two minutes and 47 seconds ahead of Iban Mayo and 5:04 clear of Linus Gerdemann, now second overall.
Alexandre Vinokourov and Andreas Kloeden both lost 4:29 while Michael Rogers crashed out of the race.
T-Mobile leader Rogers was in the same group as Rasmussen - and the race leader on the road - on the descent of the Cormet de Roseland when he hit a roadside barrier.
He bravely carried on before being forced to pull up later with a dislocated shoulder.
"It's a real shame because I could see the yellow jersey," he said.
"One moment I was in the lead, the next I was lying on the ground with my back wheel where my front wheel should have been."
Fellow Australians Stuart O'Grady and Robbie McEwen also endured miserable days.
O'Grady was taken to hospital after a crash on the same descent as Rogers while McEwen, who won the first stage in Canterbury last Sunday, was eliminated from the race after finishing outside the 40-minute time limit.
X-rays showed that O'Grady broke five ribs in the fall, as well as fracturing three vertebrae and a shoulder blade.
This could be my year as the Pyrenees are extremely difficult but, again, I need to improve in the time trials
After a stage which included three category-one climbs, Rasmussen also took the lead in the King of the Mountains competition, which he has won overall for the last two years.
After Monday's rest day he has another day in the Alps to consolidate his lead and the first time trial - the format in which he generally struggles - is not until next Saturday.
Asked if he would aim to take the yellow jersey in Paris in a fortnight's time he said: "The way I'm riding, I would be stupid not to."
"I am a pure climber so I need to grab as much time as I can in the mountains.
"When I came close to the podium two years ago, it crossed my mind I could win the Tour in the future.
"This could be my year as the Pyrenees are extremely difficult but, again, I need to improve in the time trials."
French champion Christophe Moreau was rewarded for a day of attacks on the big names with fourth place on the stage, moving up to seventh overall.
The Tour is not lost; if I had lost five minutes, it would have been over
He finished in a group with overall contenders Cadel Evans and Frank Schleck, just behind Spain's Alejandro Valverde.
However Vinokourov, still in pain after a crash on Thursday, was unable to go with those men as they chased Moreau and finished 4:29 behind the leader.
And Kloeden was ordered to help his Astana team-mate over the line even though the German had begun the day 38 places ahead of Vinokourov in the general classification, with a good chance of contending.
Vinokourov, now 22nd in the overall standings, believes he can still win the title even though he trails Rasmussen by 5:23.
"The Tour is not lost. If I had lost five minutes, it would have been over," he said.
The pace in the Alps proved too much for Britain's Mark Cavendish, who had planned to pull out at the end of the stage but in fact gave up 35km into the day.
David Millar was the first British finisher in 130th, ahead of Bradley Wiggins in 144th, Geraint Thomas in 159th and Charlie Wegelius in 172nd.
Millar lies 88th in the standings, Wegelius 104th, Wiggins 151st and Thomas 160th.
Stage eight result:
1. Michael Rasmussen (Den / RAB ) 4 hrs 49 mins 40"
2. Iban Mayo (Spa / SDV ) +2:47"
3. Alejandro Valverde (Spa / CDE) +3:12"
4. Christophe Moreau (Fra / AG2R ) +3:13"
5. Fraenk Schleck (Lux / CSC )
6. Cadel Evans (Aus / PDL )
7. Andrey Kashechkin (Kaz / AST)
8. Alberto Contador (Spa / DSC ) +3:31"
9. Denis Menchov (Rus / RAB) +3:35"
10. Carlos Sastre (Spa / CSC )
1. Michael Rasmussen (Den / RAB) 39:37:42"
2. Linus Gerdemann (Ger / TMO ) +43"
3. Iban Mayo (Spa / SDV) +2:39"
4. Alejandro Valverde (Spa / CDE) +2:51"
5. Andrey Kashechkin (Kaz / AST) +2:52"
6. Cadel Evans (Aus / PDL) +2:53"
7. Christophe Moreau (Fra / AG2R ) +3:06"
8. Alberto Contador (Spa / DSC) +3:10"
9. Fraenk Schleck (Lux / CSC) +3:14"
10. Denis Menchov (Rus / RAB) +3:19"