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The 25-year-old New York native fed off the energy of the partisan crowd at Arthur Ashe Stadium, which erupted when Pliskova returned a serve into the net on match point.
Defeat for the Czech ensured that she would no longer be top when the latest rankings are released next week.
A frustrated looking Pliskova struggled to find her rhythm throughout the match, serving just two aces while committing three double faults.
After wrapping up victory, Vandeweghe briefly fell to her knees before shaking hands with Pliskova and then walking over to her box to celebrate with her team.
"Even though we are out here individually, it's a team sport," she said in an on-court interview.
"They work as hard as I do."
Next up for the tournament's 20th seed is a showdown with either fellow American Madison Keys or Kaia Kanepi of Estonia.