Djokovic won the tournament in 2011, 2014 and 2015 but has failed to make it beyond the quarter-finals in the past two years.
Against Djokovic, his sliding across the court was almost ideal, as was his ability to disguise his angles until the last moment in what was perhaps the match of the tournament so far.
"I know now his game and I practiced with him, I watched him play".
"I'm just not thinking about tennis at the moment".
Two years ago, his career was nearly derailed when he became embroiled in match fixing allegations.
"It was an incredible, high-level match", said Zverev.
"Considering all the circumstances in the last 15 months it is quite an achievement to get to the quarters of a Slam", said Djokovic, who has also reached the Roland Garros last eight for a ninth successive year. "It's wonderful", he said.
Dominic Thiem took advantage of Alexander Zverev's depleted stamina to become the first qualifier for the men's semi-finals, beating the German 6-4, 6-2, 6-1 as the difference in court time at the competition told the story.
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Verdasco, world No. 35, coped with world No. 5 Dimitrov's winners, controlling the serve points, only conceding his service game three times out of ten opportunities.
"Obviously. making the fourth round four times or whatever is pretty good, but to finally get over that hump of quarter-finals feels very nice", she said.
"When you want to be the best player in the world and have been the best player in the world, you hate the defeats".
When pressed on whether that meant he would not play at Wimbledon, the 31-year-old Serb was non-committal. I don't know what I'm going to do.
US Open champion Sloane Stephens cruised past Estonian Anett Kontaveit 6-0, 6-2 to book a last-eight spot for the first time.
Zverev, considered among a select few capable of dethroning defending champion and French Open king Rafael Nadal, had to do it the hard way as he was on the right side of a 6-2, 3-6, 4-6, 7-6, 7-5 scoreline.
"To be able to win that first set and get ahead was crucial".
"I hope we have many more matches at the Grand Slams but when we are 100 percent". "It feels completely different here".