Caroline Wozniacki eliminated eighth-seeded American Madison Keys 6-3, 6-4 Sunday to reach the U.S. Open quarterfinals, her deepest run at a Grand Slam tournament in two years.
Edmund continued his breakthrough run at Flushing Meadows on Friday by beating American 20th seed John Isner, having already knocked out world number 15 Richard Gasquet in round one.
Djokovic will now meet Jo-Wilfried Tsonga on Tuesday in his quarter-final, once more looking on course for a clash with Murray for the title.
Lucas Pouille's upset of Rafael Nadal helped put three men from France into the quarterfinals of the American Grand Slam tournament for the first time in 89 years.
'I was pleased, ' Djokovic said in his post-match press conference after winning 6-2 6-1 6-4.
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When the draw was made more than a week ago, 21-year-old Edmund, ranked 84, fell into the Serb's quarter, but with the line-up he faced before that, any idea of a meeting between them seemed fanciful.
At the start of the third, however, he called on the trainer to massage his troublesome right elbow and there was some temporary respite for Edmund, who broke twice to lead 3-2. "I need to be ready to play my best if I want to keep going".
Edmund went on to hold serve in that game then clinched the tiebreaker with a forehand victor.
"But I made Kyle work for each point".
The match came alive in the third set when, an early break up again, Djokovic let his intensity slip and the GB number three grabbed his opportunity, finally breathing fire and showing what all the fuss is about with that sledgehammer forehand.
Edmund, nerves no doubt knocking about in his skull like pots and pans, double-faulted on his second set point but repaired the damage to go a set up just past the first half hour. I'm playing against Tsonga next match, who is a big server.
He wrapped up the first two sets in little over an hour, but Edmund produced some crunching forehands to break Djokovic's serve in the third game of the third set, prompting the top seed to seek a medical timeout. 'There's a lot of learning from this, which is a really good thing.
"It's been a great tournament for me".
"I'm sorry you guys watching didn't get to see a full match". I knew it was going to come out to one or two points.
However, he was outplayed from the start by the defending champion.
He added: "It's a little bit of an unknown because I've never played a match on that court in front of that crowd". "To play the world No1 on the biggest tennis court in the world, it doesn't get much better than that".
Bondarenko was a U.S. Open quarterfinalist in 2009 but hasn't been past the third round at a Grand Slam since.
Nadal has been impressive in NY and has shown few signs of the wrist problems which sidelined him from midway through the French Open until the Olympics.