Nadal, who lost the opening set 6-4, fought back to lead 5-3 in the second before rain forced the suspension of the match on Court Philippe Chatrier.
Marin Cilic and Juan Martin del Potro also resume their last-eight clash on Court Suzanne Lenglen, locked at 5-5 in the first set tiebreak.
World number one Simona Halep, chasing her first Grand Slam title, will take on 2016 champion Garbine Muguruza in the first women's semi-final.
Americans Madison Keys and Sloane Stephens square off in the other last-four match, a repeat of last year's U.S. Open final.
Order of play on the main showcourts (times GMT, prefix numbers denote seeding):
Court Philippe Chatrier (play starts at 1000)
Quarter-finals:
1-Rafa Nadal (Spain) v 11-Diego Schwartzman (Argentina) -Schwartzman leads 6-4 3-5.
Not before 1300
Semi-finals:
1-Simona Halep (Romania) v 3-Garbine Muguruza (Spain)
13-Madison Keys (U.S.) v 10-Sloane Stephens (U.S.)
Court Suzanne Lenglen (play starts at 1000)
Quarter-finals:
3-Marin Cilic (Croatia) v 5-Juan Martin del Potro (Argentina) - match tied 6-6 (5-5)
Mixed doubles - final
1-Gabriela Dabrowski (Canada)/Mate Pavic (Croatia) v 2-Latisha Chan (Taiwan)/Ivan DODIG (Croatia).
Men's doubles - semi-final
8-Nikola Mektic (Croatia)/Alexander Peya (Austria) v 6-Pierre-Hugues Herbert (France)/Nicolas Mahut (France)
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Toby Davis)
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