That initial burst gave Federer 34 successive sets won at Wimbledon, equaling his own record set between 2005 and 2006.
A year after his 2017 fourth round match was postponed by 24 hours into what is a designated "rest day" for the men, he narrowly avoided suffering the same fate again.
Rafael Nadal awaits in the semifinals after the Spaniard took the scenic route in a five-set marathon against Juan Martin del Potro; a rematch of the 2011 contest where Djokovic first tasted success on the lawns of south west London. It was Federer who blinked, double-faulting to face a break point at 11-all, then slapping a forehand into the net.
"Luckily for me it didn't happen", Djokovic said after he romped to a 6-4 6-2 6-2 win to reach the last eight for a 10th time.
Djokovic, victor of three singles titles at the All England Club, will next meet Japan's 24th seed Kei Nishikori.
"It's not the first time in the semi-finals - I've been here before - but first I'll try to enjoy this victory before thinking about the next opponent".
"It was just one of those days where you hope to get by somehow", said Federer, who last played at No. 1 Court in 2015.
'I didn't harm the grass. However, Djokovic was unable to maintain his level and it was Nishikori who broke for 3-1 and took the second set.
Djokovic was seen engaged in a heated discussion with the umpire in the aftermath of the warning and it is fair to say some of his comments and complaints have left a sour taste in the mouth of some Wimbledon punters over the course of the championships.
"Post-match I heard that the organisers were planning to cancel my match if Monfils and Anderson went to a fifth".
Seeded 12, Wednesday will Djokovic's 41st appearance in a Grand Slam quarter-final.
"I feel if I have to compare the game that I've played, the level of tennis that I've had those years and today, I think it's pretty close", he told reporters after two and half hours on a sunny Centre Court.
'I feel like I'm peaking at the right moment.
Djokovic had four break points in the first two service games alone and suffered a Wimbledon meltdown as he bounced his racket off the ground, argued with the umpire, and then went on to lose the second set. I haven't spent too much time on the court.
Djokovic is a three-time victor at Wimbledon, having won the title in 2011, 2014 and 2015.
Djokovic spent a lot of time on the sidelines recovering from a terrible elbow injury that had many fans worrying that he may never return to his scintillating best. I know, as everything in life, we are evolving.
"Double standards, my friend".