It was the first set Nadal had lost in his last 38, stretching over three French Open campaigns - meaning Bjorn Borg's record of 41 straight sets won remained intact.
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.
But Schwartzman was in no mood to give up and broke the Spaniard twice in the seventh and the ninth game, with Nadal earning a break of his own in the eighth.
Nadal, aiming for an 11th French Open title, trails the 11th seed 6-3 3-5.
The world number one has also won 37 consecutive sets in this tournament, although he needed a tie-break in the third set to secure the win over the world number 70.
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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.
Nadal made 14 unforced errors and struck just four winners in a poor first set, before having both of his wrists strapped by the trainer.
In the second quarter-final Marin Cilic and Juan Martin Del Potro were locked together at 5-5 in a first-set tiebreak.
The enforced interlude had clearly benefited Nadal, and assuming he gets the two points he needs to level the match he will start a strong favourite on Thursday.
"The amount of stress you can imagine he was under when he left the court for the first time", she said. After a brief rally of handful of forehands, the ball boy seemed to have had enough of it, but Nadal insisted on playing another point and this time the ball boy brought out his double-handed backhands.