The American, seeded 24, won the last-16 match 7-6(4) 6-4 to advance to the quarter-finals. She was more aggressive and took more risks than Wozniacki, and her strategy paid off - she fired 38 winners across the net compared with her opponent's 16.
She credited her increased focus on court to her coaching partnership with former Wimbledon champion Cash, who she hired in the run-up to the tournament.
"He's kept the same kind of mantra through the start of us working together ... of focusing - it's kind of the demand he has," Vandeweghe said of the Australian, adding that he had spent Sunday night celebrating the 30th anniversary of his 1987 victory at the championships.
"I'm going to do everything in my power to give what he's asking."
By reaching the quarter-finals, 25-year-old Vandeweghe has matched her best performance at the All England Club. She will be the favourite against 87th-ranked Magdalena Rybarikova, even though the Slovak beat her at the French Open in May.
Against Wozniacki on Monday, there was little between the two players in the first set, which Vandeweghe edged in the tiebreak. She closed out the match with a break at the end of the second set, forcing an error from her Danish opponent with a ferocious crosscourt forehand.
Wozniacki, who had beaten Vandeweghe in their two previous encounters, said she had nothing to prove to the outside world.
"I don't play tennis for anyone else, I play for myself. I love being out there. I'm not there to prove anything to anyone except for myself," said the 26-year-old, who has finished two seasons as world number one - 2010 and 2011 - but has never won a grand slam.
"It was a tough match, it was close. Maybe if I'd gotten that first set tiebreaker, maybe it would have been different."
(Reporting by Pravin Char; editing by Mark Heinrich and Pritha Sarkar)
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