Sainz beat American Volkswagen teammate Mark Miller by three minutes, 41 seconds to secure his third stage win of the race.
Another American, Robby Gordon, finished third in his Hummer after the shortened 243km stage from Argentine city Mendoza to Chilean capital Santiago.
However, there was drama as two of the race favorites lost any chance of winning. Nasser Al Attiyah of Qatar, who led at the end of Thursday's stage, was disqualified for missing two control points. Al Attiyah had won the first and third stages of the race.
Then defending champion Stephane Peterhansel of France had to put out a fire in the engine of his Mitsubishi after 57km. He was able to resume briefly before his engine broke down again, and looked likely to abandon the race.
Meanwhile, Giniel De Villiers of South Africa, who took the race lead after Al Attiyah's disqualification, finished sixth on Friday and lies just nine seconds behind in the overall standings.
Chile's Francisco Lopez pleased the home fans by edging Marc Coma of Spain, who retained the overall lead, in the motorcycle section. American Jonah Street is second overall, while Lopez is up to 10th place.
The rally is being held in South America for the first time after being canceled in 2008 because of the threat of terrorist attacks along its traditional route through Africa.