Sastre began the race as an outsider, but his consistency — thanks to the textbook support work of his strong CSC team — proved key.
On the penultimate stage time trial, he held his nerve to keep a faltering Evans in his wake.
Compatriot Alejandro Valverde, one of the big pre-race race favorites with Evans, dropped out of virtual contention on the 10th stage.
On the second of three days in the Pyrenees, the pace of CSC proved too much for Valverde, who finished five minutes off the pace of stage winner Leonardo Piepoli.
“I expected to do better at this Tour and would have liked to have been on the podium,” said Valverde, who finished sixth overall last year having crashed out injured in two previous participations. “But I’ll be going away with good memories of my stage win and the yellow jersey, and I’ll be back next year.”