But the 33-year-old Spaniard, who is mainly known for his climbing skills, managed to claim 12th place in the time trial, 2:34 behind Schumacher.
Evans could only finish seventh, shaving just 29 seconds off his rival's lead.
Barring a major mishap on the final stage to Paris on Sunday, Sastre will become Spain's third successive Tour de France champion after Alberto Contador last year and Oscar Pereiro in 2006.
Sastre, who took the yellow jersey courtesy of a bold attack in the ascent to l'Alpe d'Huez in Wednesday's last alpine stage, leads Evans by 1:05 going into the traditional parade to the Champs Elysees.
|Australian Evans failed to chase down Sastre's lead [AFP]
"I just tried to stay calm throughout the whole race," Sastre, who finished third on the race two years ago, said. "It was the chance of a lifetime and I knew I had to fight with every last drop."
Evans was the fourth last to start from the field, but by the time Sastre past the first time check after 18km the writing was already on the wall for the 31-year-old Australian.
With just over a third of the course completed, he had managed to take only eight seconds off his Spanish rival.
Evans sped up over the second half of the rolling course between Cerilly and Saint-Amand-Montrond, however Sastre dug deep and managed to retain most of his advantage.
Evans, who finished the tour in second place last year, said he was disappointed .
"I had a good day, a good start - the first time check I got after six kilometres I was doing the same time as Cancellara, for me was a really really good indication."
The Australian put the defeat down to the strength of Sastre's CSC team.
"It comes down also to the fact they have two, two and a half times the budget we do, and straight away that can buy much better quality riders," he said.