The 28-year-old Ukrainian looked helpless against the Spaniard's dominant serve, which was boosted by courts made faster due to sunny conditions at the Arthur Ashe Stadium.
"I think I played a solid match. I played without making many mistakes," Nadal told the crowd in an on-court interview.
Next up for the top seed is a first meeting with 19-year-old Russian Andrey Rublev who beat Belgian ninth seed David Goffin.
Nadal dominated all facets of Monday's match, never dropping a service game and committing only 11 unforced errors while racking up 23 winners and breaking Dolgopolov six times.
The onslaught was too much for the unseeded Dolgopolov, who was never comfortable enough to unleash his unconventional game that features unexpected drop shots and bold net approaches.
(Reporting by Rory Carroll; Editing by Ken Ferris)
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