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The Spaniard, also looking to match Roger Federer's record of 20 Grand Slam men's singles titles, was stretched like rarely before by the 19-year-old Sinner as he set up a clash with Argentine Diego Schwartzman, who beat him in the Italian Open quarter-finals last month.
The 34-year-old Nadal's 97 previous victories at Roland Garros made the difference in the key moments with the Spaniard rallying from a break down in the first two sets.
Sinner, the first French Open debutant to reach the last eight since Nadal in 2005, confirmed his immense potential but lacked just a bit of composure when it mattered.