Having edged two tiebreaks late on Sunday before being beaten by the tournament's strict 11pm curfew, the Serb returned to lose his first set of the tournament before sealing a 7-6(6), 7-6(6), 5-7, 6-4 victory.
Djokovic was not at his best as Hurkacz briefly threatened a comeback but, as he so often does, the record 23-time Grand Slam men's champion found a solution.
He has now moved equal in second place with Jimmy Connors for Wimbledon quarter-finals reached and will face Russia's seventh seed Andrey Rublev on Wednesday.
Remarkably the Serbian has now reached 56 Grand Slam quarters-finals, second behind only Roger Federer.
With wind swirling around Centre Court, Djokovic struggled for his usual rhythm and dropped serve for the first time in the match to hand over the third set.
The second seed looked uncomfortable for a while against the 17th seed, who ended Federer's Wimbledon career two years ago.
But Djokovic pounced to finally the break the Hurkacz serve for the first time at 3-3 in the fourth -- having seen seven previous break points snatched away.
From then on it was straightforward as Djokovic quickly wrapped things up in clinical fashion.