The top two men - Andy Murray and Novak Djokovic - and three of the top four women - Kerber, Aga Radwanska and Simona Halep - have departed in the Open's first week.
Serena Williams will now be a prohibitive favourite to claim a seventh crown at Melbourne Park, but on the basis of Vandeweghe's showing, she could also go all the way.
"It's really special to play a number one player in the world on any stage. I believe its my first number one win so i'll take that," she said.
The shock result leaves the men's draw wide open after defending champion Novak Djokovic was earlier eliminated in the second round.
It is the first time since 2004 that the top two men's seeds have failed to reach the quarter-finals of a grand slam, and the first time tit has happened at Melbourne Park since 2002.
Zverev was cheered on by his younger brother Alexander, who was considered by far the most likely of the pair to make a deep run at the Open before his agonising five-set loss to Rafael Nadal on Saturday.
But it was the older sibling who shone in the spotlight on Sunday, stunning Murray with the performance of a lifetime in his sixth Open appearance having never previously made it past the second round.
The 29-year-old's reward for his career win is a quarter-final shot at either four-times champion Roger Federer or fifth seed Kei Nishikori, who play their fourth-round match on Sunday night.
"I don't know yet how I feel because everything is new to me and everything feels a little bit unreal," Zverev said.
Murray was far from his best against the unheralded left-hander, struggling with his second serve and growing increasingly frustrated by his seeming inability to read the German's play.
It is the first time in more than a decade that Murray has been defeated at a grand slam by someone ranked as lowly as Zverev.
"It just wasn't meant to be," the Scot said.
"He served very well when he needed to, especially when he was behind in games. He deserved to win.
"He came back from all of the mistakes that he made, kept coming up with great shots. There's not too much you can do about that. It was obviously disappointing to lose. But he did some good stuff out there."
With an opportunity to take a 5-3 lead in the fourth set, Zverev looked like nerves may get the better of him, hitting a simple forehand smash into the net.