A rare couple of wobbles failed to derail Rafael Nadal, who overcame the spirited challenge of Maximilian Marterer to reach the French Open quarter-finals with a 6-3, 6-2, 7-6 (7-4) success on Monday.
Cecchinato, the world No 72 who bundled the former champion Novak Djokovic out of the tournament on Tuesday, gets his chance to go forward on Thursday, when he plays Dominic Thiem in the first semi-final.
After a rain delay midway through the second set, play was finally stopped for the day with Nadal serving for the set at 5-3 30-15.
Schwartzman, the 11th seed, was certainly playing out of his skin, but even that should have not been enough to trouble a Nadal playing anywhere near his peak.
The 37-set run was Nadal's longest at the French Open, where the record of 41 was established by Bjorn Borg from 1978-81.
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He had lost the first set and was a break down in the second before returning from a one-hour interruption to turn the tables on Schwartzman and gain the upper hand.
Nadal had to receive treatment to his wrist at the end of the set with extra strapping applied.
A more serene start to the second set all changed when Nadal again dropped his serve at 1-1, and just as in the first while he recovered immediately, Schwartzman broke again for 3-2.
Nadal and Schwartzman will resume their enthralling last-eight match at 12:00 local time on Thursday, with the 25-year-old Argentine seeking to become only the third player ever to beat Nadal at Roland Garros.
On Suzanne-Lenglen, Marin Cilic's last-eight tie with Juan-Martin Del Potro failed to burst into life until the ninth game, when the Croatian saved three break points before eventually holding, and did likewise in his next service game before taking the set to a tiebreak - which was locked at 5-5.