The big-serving Czech’s 17-match losing streak to the Spaniard was the equal longest in the professional era and after fending off Nadal in a tight third set, the seventh seeded Czech revelled in his “Vitas Gerulaitis moment”.

"I start pretty well, but you’re playing Rafa and you have to keep going to the last point," the 29-year-old said. "We set up the great plan for today’s game and it worked.

"I’m just putting myself in the best possible position right now, really trying to go one by one."

The first two sets were over in exactly an hour, with Berdych serving masterfully, saving all four break points conceded and sealing the match with a raking second serve that Nadal could only bunt back into the net cord.

On the comeback trail after injury and illness, Nadal battled hard to save three match points, but his second set whitewash was his first bagel since playing great rival Roger Federer at the 2006 Wimbledon final, adding to the surreal atmosphere over centre court.

"It was just not my day. I didn’t play with the right intensity, the right rhythm," Nadal said.

"It was a day when the opponent played better than me.

"I made him play very easy so you cannot expect to win quarter-finals ... helping the opponent to play well."

Berdych will play the winner of sixth seed Andy Murray and local hope Nick Kyrgios, who clash in the evening session.

Though similarly one-sided, it was old stager Sharapova maintaining her domination in the earlier quarter-final.

Bouchard said she had learned a lot from her gutting French Open loss last year when Sharapova overhauled her from a set down, but nothing could have prepared her for the 78-minute demolition that Sharapova inflicted upon her.

The Canadian wore a look of grim determination as she waited in the player’s tunnel to make her centre court entrance, but it was masking a head full of nerves.

She double-faulted and committed two unforced errors to gift three break-points in the opening game. Her opponent used just one to break her before charging to a 3-0 lead.

Completely dictated, Bouchard had nowhere to hide from her second serve which the strong-willed Russian feasted upon.

Sharapova was stingy, giving up only two break points for the match, none in the first set, and saving both.

In full flight, she swooped in for the kill with a string of smoking winners, sealing it with a crunching inside-out forehand.

As Sharapova blew kisses, Bouchard headed straight for the exits, biting her lip.

"Am I happy that I was able to lift my game after having a couple matches where I wasn’t satisfied? Yeah, absolutely," Sharapova said.

"But the toughest is what’s to come. I hope that I’ll be able to take that and play even better."

It was a depressingly similar story for third seed Halep, who had cruised into the quarter-finals by smiting a succession of lower-ranked opponents.

She ran head-first into a brick wall in the form of lithe left-hander Makarova, a grand slam doubles champion who announced herself with a run to last year’s semi-finals at Flushing Meadows.

Halep also has major credentials, reaching last year’s French Open final and favoured to go one step further in time.

Instead, she froze, later admitting she had felt "a little bit too stressed" before a ball was struck.

Makarova, however, was a bouncing, hustling ball of energy. She broke twice for a 3-0 lead before her opponent had blinked, pouncing on anything short and despatching the Romanian’s top-spin bombs with disdain from the baseline.

The Russian lost focus only briefly in the second set, falling 0-40 in the second game, but saved all three break points before motoring to victory in 69 minutes.

The 26-year-old lefthander, who describes herself as shy off-court, has not lost a set all tournament. Her matches have lasted a tick over one hour and 11 minutes on average and she will head into her clash with Sharapova fresh and in top form.

"I’m not shy on the tennis court. It’s a big stage," she said. "I never beat (Sharapova), so it will be tough."