The Spaniard, looking to claim a record-extending 14th Roland Garros singles title and become the only man with 21 Grand Slam singles crowns, has won 35 consecutive sets in Paris.
World number 19 Sinner, who at 19 years old has been labelled as the next big thing in tennis, hit a brick wall on court Philippe Chatrier after leading 5-3 in the opening set.
Third seed Nadal will now face Argentine Diego Schwartzman for a place in the semi-finals.