Sastre, 33, dropped the maillot jaune group 13km from the summit of the infamously steep Alpine climb, and none of the main contenders for victory were prepared to follow him.
Andy Schleck and Samuel Sanchez came in two minutes and three seconds behind Sastre, who took the second Tour de France stage victory of his career.
In the 25 previous summit finishes at Alpe d’Huez, the man wearing yellow on the podium has gone on to win the Tour 19 times.
Team CSC may now have to rethink their strategy, with Sastre 1min 24sec ahead of Frank Schleck in the general classification and the potentially decisive time-trial from Saint Amand to Cerilly to come on Saturday.
Cadel Evans, a formidable time-triallist, is still within reach, 1:34 behind Sastre overall.
Frank Schleck was unable to put clear distance between himself and Evans, despite the best efforts of his younger brother Andy and Caisse d’Epargne’s Alejandro Valverde.
Valverde repeatedly tried to pull Schleck away from Evans, but the Luxemburger was unable to produce the crucial kick that could have given him breathing space for the stage against the clock.
Sastre was more than a minute slower than Evans and Denis Menchov in the first time-trial at Cholet, which could make for a nailbiting finish if he maintains his 84-second advantage when the peloton reaches Cerilly.
Said Sastre: “We have seen a great stage, and a team which worked perfectly.
“Without the support of Frank and Andy, none of this would have happened.
“We had to choose the right rhythm at the foot of the last climb, and accelerate later. Normally, a good climber is able to capitalise on this sort of situation, and that’s what happened.
“I don’t know if I have the crucial advantage, we’ll see what happens in the time-trial on Saturday.”
Bernhard Kohl, the revelation of this year’s Tour, also remains in contention, sandwiched between Frank Schleck and Evans in third place.
The young Austrian from Gerolsteiner cemented top spot in the King of the Mountains competition, opening up a 45-point lead on Frank Schleck and Sastre, with the CSC duo expected to concentrate on the general classification.
Stefan Schumacher led over the Col du Galibier, but Peter Velits dropped the German on the long climb up the Col de la Croix de Fer, and Jerome Pineau joined the Slovakian to begin the steep ascent up Alpe d’Huez.
But they were swallowed up as Sastre roared up the hill with Menchov on his wheel. Menchov initially dropped back under the strain, but came back to finish in the same time as Evans.
Though the Russian possesses time-trialling ability to rival the Australian, he is now two minutes 39 seconds behind yellow and surely out of reach.
Earlier, German air conditioning manufacturers Saunier Duval announced they were ending their involvement in cycling sponsorship.
The Saunier Duval-Scott team withdrew from the Tour in the wake of Riccardo Ricco’s positive test for EPO.