Djokovic into 14th Wimbledon quarter-final
Defending champion Djokovic, chasing a record-equalling eighth title and 24th Grand Slam, won 7-6 (8/6), 7-6 (8/6), 5-7, 6-4.
In the fourth set, Djokovic broke for a crucial 4-3 lead, ending Hurkacz's perfect run of 67 service games at the tournament this year.
Victory in his 100th match at the tournament gave Djokovic a 90th win.
He is also on a 32-match win streak at the All England Club, while his 56th Grand Slam quarter-final spot is second only to the 58 of Roger Federer.
"Big credit for Hubert for playing an amazing match, he put up a great performance," said 36-year-old Djokovic.
"Honestly I don't recall the last time I felt this miserable on returning games. He has one of the best serves in the world and it's difficult to read it on one of the quickest surfaces in the sport. It was not enjoyable for me."
Djokovic will face Andrey Rublev for a place in the semi-finals.
That match will take place on Centre Court, where Djokovic has not lost since 2013.
"I feel a great connection with this court. Every match that I win, every time I step on the court I feel more confident to play the match and hopefully the love affair continues for a long time," he said.
Djokovic had been two sets up overnight when the match was suspended due to a local curfew.
He had squandered five break points in those sets and Hurkacz eventually made him pay by breaking in the 12th game of the third set on Monday.
But Djokovic hit back to break for 4-3 in the fourth and from then on there was no way back for the 17th-seeded Pole despite his 33 aces and 64 winners.
Djokovic will take a 3-1 career lead over seventh-ranked Rublev into their quarter-final on Tuesday.
Djokovic came out on top in straight sets at the same stage of this year's Australian Open.
"He's a different player to Hurkacz for sure," said the Serb.
"Very powerful, very quick ground strokes, loves to dictate. I'm not going to talk to much about tactics -- I will to keep that to myself."