Murray had not beaten a top-10 player since his emotional victory over Djokovic on Centre Court more than a year ago but played a very fine match in the New York heat to defeat ninth seed Jo-Wilfried Tsonga 7-5 7-5 6-4.
It maintained the Scot’s impressive record of having reached at least the quarter-finals of every grand slam tournament he has played in for the past four years.
Murray had beaten Tsonga in nine of their previous 11 matches but lost the most recent one in Toronto last month from 3-0 up in the final set.
It was the first time Tsonga had beaten his former junior rival in a competitive match for six-and-a-half years.
The Frenchman revealed ahead of the clash that there was no longer the same fear factor about Murray in the locker room, and he also sensed there was not the same power in Murray’s serve and groundstrokes.
“It was extremely tough conditions, very humid,” said Murray.
“It started to cool down a bit at the end but the first two sets were very long, tough sets and mentally quite draining. I’m glad I managed to get through.”
The 27-year-old will meet his long-time rival Djokovic at a slam for the first time since Wimbledon in the last eight on Wednesday and for the first time at Flushing Meadows since his maiden grand slam triumph two years ago.
“It will be a tough match,” said Murray.
“We’ve had a lot of long ones, there are normally a lot of rallies. We had a long one here a few years ago; I’ve obviously got great memories from that match.
“Hopefully we can play another top-level match. If I play well, I have a chance.”
Men’s world No 1 Djokovic moved into the quarter-finals of a grand slam for the 22nd time in a row after seeing off Philipp Kohlschreiber.
The 22nd seed, from Germany, was the last man to deny Djokovic a place in the last eight of a major tournament, beating him in the third round at Roland Garros in 2009.
But he had no answer this time around.
Djokovic made a lightning start, winning the first four games, and although Kohlschreiber began to find some rhythm he could do nothing to prevent a 6-1 7-5 6-4 victory for Djokovic.
“It was very humid for both of us,” said Djokovic said.
“We had a lot of long rallies and the match could have gone either way, especially in the second set.”
In the women’s draw, Serena Williams reached her first grand slam quarter-final of the year with a comfortable victory over Kaia Kanepi.
So far there have been none of the wobbles that led to unexpected defeats for the world No 1 in Melbourne, Paris and at Wimbledon.
She has not lost more than three games in any set and was a relatively comfortable 6-3 6-3 winner over her opponent.
In the last eight, Williams will face 11th seed Flavia Pennetta, who is having another good run at Flushing Meadows.
The Italian has only made one quarter-final at all the other grand slams combined, but is through to her fifth in New York after a 7-5 6-2 victory over Casey Dellacqua.
“Everyone asks the same question,” said Pennetta. “I don’t know. I just like to play here and maybe that’s why I play good here.”