World number two Alcaraz dominated from the start with aggressive baseline play and several spectacular shots that made the audience cheer.
Rinderknech, ranked 82nd in the world, looked noticeably tired at the end of the match.
I found a good rhythm and it was just to continue, says Alcaraz after the match.
He also took the opportunity to flirt a bit with the American audience.
I think my playing style fits very well with the energy here in New York. The energy is always special here, he says.
The 21st-ranked Czech Jiri Lehecka now awaits in the quarterfinals, on Tuesday.
22-year-old Alcaraz is chasing his second title in the tournament. The first one he took in 2022.
