Djokovic stays on track for Wimbledon glory under Federer gaze
Djokovic was lethargic and unusually tentative in the early stages of his last-16 match against the Australian 11th seed on Centre Court, but eventually found his rhythm to win 1-6, 6-4, 6-4, 6-4.
It keeps the seven-time champion on track for a record-breaking 25th Grand Slam title, which would be the crowning achievement of an astonishing career.
If he wins the crown on Sunday, the 38-year-old Serb would also draw level with Federer's record of eight men's titles at the All England Club.
Retired Swiss great Federer watched from the royal box as his long-time rival was given his toughest test of the tournament so far.
"It's probably the first time he's watching me and I've won the match," said Djokovic. "The last couple I lost, so good to break the curse.
"No, it's great, obviously, great to have Roger, a huge champion and someone that I admired and respected a lot.
"We shared the stage for so many years, and it's great to have him back."
Sixth seed Djokovic was broken in the first game and conceded two more breaks as De Minaur ran away with the first set.
The Serb committed 16 unforced errors, including four double faults in the opener.
Djokovic broke immediately at the start of the second set but then became bogged down in a game lasting nearly 19 minutes, which De Minaur won on his sixth break point.
Both players struggled to hold onto their serve in an attritional battle but Djokovic, pleading for support from the crowd, held his nerve to level the match, letting out a roar as De Minaur went long.
The third set went with serve until the ninth game, when De Minaur skewed a forehand wide to concede the crucial break.
De Minaur found new inspiration in the fourth set, surging into a 4-1 lead but crumbled at the pivotal moment as Djokovic fought back, reeling off five games in a row to seal the win in three hours and 18 minutes.
"I'm still trying to process the whole match and what happened on the court," he said. "It wasn't a great start for me, it was a great start for him obviously.
"I was just very pleased to hang in tough in the right moments and win this one."
Djokovic's tally of 16 Wimbledon quarter-finals is second only to Federer's total of 18 in men's tennis.
He will play Italian 22nd seed Flavio Cobolli in the last eight, with a potential semi-final looming against world number one Jannik Sinner.