The Russian fourth seed, Wimbledon champion as a 17-year-old in 2004 but a finalist only once since, had not dropped a set in this year's tournament coming into the last-eight contest.
However, after a relatively untroubled first set on Centre Court, she lost a hugely entertaining second as the two identikit 6ft-plus blondes with matching white visors slugged it out.
Vandeweghe, the only unseeded player in the last eight, showed plenty of grit, not least when breaking as Sharapova served for the match at 5-4 in the second set, whipping up Centre Court crowd in the process.
Sharapova then displayed her own fighting spirit when, despite again struggling with her serve, she twice saved set point before Vandeweghe's fearless deep hitting earned her the tiebreak and dreams of an upset victory.
In the final set Sharapova quickly seemed to take control with a break in the second game to race to a 3-0 lead but Vandeweghe refused to lay down or ease off and broke back to trail 3-2, again urging the crowd to get behind her as she marched back to her chair.
Sharapova had struggled for consistency all day but put together a run of aggressive, accurate returns together to break again for a 4-2 lead and then landed a rare ace to finish off her next service game to make it 5-2.
This time there was no coming back as Sharapova then broke again to take the match and set up a semi-final against either top seed Serena Williams or Victoria Azarenka, who were meeting on Centre Court later on Tuesday.
"I was pretty dominant in the first and early in the second set but things slipped away," said the five-times grand slam champion.
"She's playing with a lot of confidence but I really regrouped in the third.
"You have to give everything you have on a special occasion on a special court.
"It's been a while since I've been at the semi-final stage (at Wimbledon) so I'm really happy."
(Editing by: Pritha Sarkar)
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