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 top the WTA rankings when they are released next week.
Pliskova looked frustrated and struggled to find her rhythm throughout the match, serving just two aces while committing three double faults and 21 unforced errors.
"I can play much better than I was playing today. I didn't feel the best," she said in a post-match news conference.
"But I think you're never going to feel your best with the game that she's playing."
Vandeweghe smacked 24 winners, most of them coming from her powerful forehand, while rocketing five aces and saving five of her seven break points.
After wrapping up victory, Vandeweghe briefly fell to her knees before walking over to her box to shake hands and exchange words with her coach, former Wimbledon champion Pat Cash.
"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 20th-seeded Vandeweghe is a showdown with either fellow American Madison Keys or Kaia Kanepi of Estonia.
(Reporting by Rory Carroll; Editing by Toby Davis)
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