The 16th seed became the first Israeli woman to reach the quarter-final of a grand slam with a performance of great agility on Vodafone Arena, often cruelly exposing the lethargic movement of her flat-footed Russian opponent.
The 19-year-old broke the Russian's serve three times in a scrappy opening set and even a five-minute rain interruption while she was serving at 4-2 in the second failed to disrupt her concentration.
She bravely served out against the increasingly frustrated former US Open champion, and a netted forehand from the third seed spelt the end after 77 minutes on court.
Shahar Peer celebrates (Photo: AP)
"I've never beaten this kind of top 10 player before," said Peer, already a semi-finalist on the Gold Coast this year.
"I went to play my game today and I am very happy with the way I played. My serve was effective, I was aggressive and the rain delay did not affect me."
Kuznetsova had steamrolled her opponents in the first three rounds for the loss of just 10 games, and even had a slim chance of claiming the world number one spot if she went on to win the title.
But Peer, who reached the fourth rounds at the French and US Opens last year, ensured there was no chance of that with exceptional speed at the back of the court contrasting sharply with Kuznetsova's laboured movements.
Peer will now face the winner of the fourth-round match between in-form Serbian 11th seed Jelena Jankovic and twice former champion Serena Williams.