The 31-year-old has only lost two matches in his career at the tournament and he used his relentless aggression from the baseline to wear down the determination of Schwartzman to secure a further two breaks to move within a game of the last four. In the other quarterfinal, Marin Cilic and Juan Martin del Potro were into the tiebreak and at 5-5.
He went on to break Nadal two more times in the second set before the match had to be stopped due to rain. Schwartzman saw two set points come and go but at the third time of asking, after a delay while a spectator was helped out after feeling ill, the Argentine ripped a forehand victor.
Another rain delay sent the players off court and shortly afterwards play was suspended for the day.
The top-ranked Spaniard beat unseeded Maximilian Marterer 6-3, 6-2, 7-6 (4).
Nadal returned with his famed forehand finally firing on all cylinders, earning back-to-back breaks to move within a hold of the set.
French Open 2018: Muguruza dumps Sharapova to reach semis
Muguruza sensed weakness and pounced for a 4-0 lead. "I was focusing on winning every point, every game", Muguruza said. Kerber would become only the second German woman to reach the last four in Paris since Steffi Graf won back in 1999.
Kasatkina raced away with the last three games of the tie which had been halted at 3-3 in the second set late Sunday because of bad light.
They will return on Thursday morning.
With Halep having outlasted Angelique Kerber on Wednesday, 6-7 (2-7), 6-3, 6-2, then looked at her coach while pointing to her head, she and Muguruza grace the bracket opposite the all-American match between Sloane Stephens and Madison Keys, the 2017 US Open finalists who have their own curious paths.
The top seed had few problems in serving out the set and he made a flying start to the second with another break to love as Marterer got a first-hand look at why the champion has been dubbed the King of Clay.
The Romanian broke serve six times against a player who made the semi-finals at the Australian Open in January.