The 23-year-old world number seven knew his hopes of reaching the semi-finals would be as good as over if he suffered a second loss, having been beaten by Daniil Medvedev on Monday.
While there were still a few lapses, Zverev ultimately had too much firepower for the debutant from Argentina.
Just as he had done against favourite Novak Djokovic on Monday, Schwartzman got an early break of serve only to fall away in disappointing fashion as 2018 champion Zverev broke back twice to take the opening set.
Playing in front of 18,000 empty seats, both players lacked sparkle in a subdued contest but Zverev looked on course for a comfortable win as he led 3-1 in the second set.
The German appeared to lose focus though and Schwartzman grabbed his chance to win five of the next six games and extend the match into a…