Swiatek, fresh from a fourth French Open title, came through 6-3, 6-4 against her 49th-ranked American opponent, a former Australian Open champion.
The top-seeded Pole, chasing a sixth Grand Slam title, has yet to get beyond the quarter-finals at the All England Club.
She will face either British wild card Francesca Jones or Petra Martic of Croatia for a place in the last 32.