Prerace favorite Cadel Evans of Australia was unable to overcome his deficit of 1 minute, 34 seconds to Sastre entering the stage despite being considered a superior time trialer.
Sastre made the sign of the cross, kissed his fingers and shook them skyward as he crossed the finish line after the 32.9-mile race against the clock.
"This is the dream of my life that's become a reality now," said Sastre, who finished in the top 10 in five of his previous seven Tour appearances. "At the end of the race, I was feeling better and better and was in top form at the end of this week."
The Spaniard credited his teammates with helping him conserve energy for the time trial by sheltering him from the wind in the stages after he took the yellow jersey Tuesday in the last Alpine segment.
Overall, after more than 84 hours of racing since the July 5 start, Sastre led Evans by 1 minute, 5 seconds, while Bernhard Kohl of Austria was third, 1:20 behind.
Sunday's final stage - an 88.9-mile ride from Etampes to the Champs-ElysDees in Paris - is likely to be a ceremonial ride won't change the overall standings. Traditionally, attacks on the leader are frowned upon and any attempts at a breakaway by a rival are easy to counter on the flat course.
This is the second straight year that the Tour has seen one of its tightest finishes ever, with the lead up for grabs going into the final time trial - giving some much-needed drama to an event that has been dogged by doping scandals for several years.
Three riders, including Italian star Riccardo Ricco, were kicked out of the race during the first week. Sastre, however, insisted unequivocally that "I'm clean."
"There have been cheaters in the past, and there always will be," he said through a translator. "But there are people who work silently, with honesty, and who are outside of all these controversies."
Sastre is poised to become the third Spaniard in a row to win cycling's premier race. Alberto Contador won last year and Oscar Pereiro inherited the 2006 title that Floyd Landis of the United States lost in a doping scandal.
Evans, who trailed Contador by only 23 seconds last year, appears set for his second straight second-place finish.
Schumacher clocked 1 hour, 3 minutes, 50 seconds in the stage, and was followed by CSC rider Fabian Cancellara of Switzerland, 21 seconds behind, and Kim Kirchen of Luxembourg in third, 1:01 back.
Evans was seventh, 2:05 behind, and Sastre was 12th, 2:34 back.
"Everything was good this morning," Evans said. "I had a good start, the first time check I got was the same time as Cancellara, which was a really good indication. I thought, 'Golly, I'm on a good day here.' "... I will be back next year. I think I have three or four good Tours left in me."
