The 7-6 (8-6) 6-3 3-6 6-3 victory moved the 39-year-old clear of his retired rival Roger Federer on the men's all-time match wins list at the grass court grand slam.
The seventh seed will now have another piece of history in his sights as he bids to equal the Swiss great's haul of eight Wimbledon titles.
"Survive to thrive, that's how I feel," Djokovic said during his on-court interview when asked to reflect on week one of the championships.
"Hopefully the thriving part is coming!"
But it was far from smooth sailing for the seven-time champion under the blazing sun on Centre Court, as he twice dropped serve with uncharacteristic mistakes, before saving two set points at 2-5 down to win the first set in a fiercely contested tiebreak.
World No.132 Safiullin, eyeing a major upset after months out with a hip injury, continued to test Djokovic but crashed his backhand into the net to fall behind 2-4 in the second set.
Having found the opening, Djokovic quickly doubled his lead in the match with some exquisite serve-and-volley tennis, before his frustrations boiled over when Safiullin broke and snatched the third set to extend his adventure.
After a tight hold to start the fourth set, Djokovic took his level up a notch to complete the win.
"Another hard-fought win. Roman started very well. He was very aggressive, so I didn't maybe feel as comfortable from the back of the court," Djokovic said.
"I haven't felt inferior from the back of the court with too many players, to be honest, throughout my career. Today it was one of those days where I didn't want to stay in the rally for too long.
"In the end, I managed to find the accuracy and precision on my first serve, which really got me out of trouble in the fourth set."
It may have been ugly, but the ageless Djokovic is through to his 17th Wimbledon quarter-final and one step away from a possible semi-final showdown with defending champion and top seed Jannik Sinner, who comfortably saw off Japanese qualifier Shintaro Mochizuki 6-3 7-6 (7-0) 6-3.
For that to happen Djokovic will have to beat Canadian third seed Felix Auger-Aliassime, who outlasted Spain's last survivor Alejandro Davidovich Fokina 6-7 (4-7) 7-6 (8-6) 6-3 6-7 (2-7) 6-1 - a four-hour 26 minute battle that ended with an angry exchange of words between the players at the net.
Sinner is yet to face a seed and will not do so in the quarter-finals, where he will play veteran Jan-Lennard Struff.
The German reached the last eight at a grand slam for the first time, at his 47th attempt. The 36-year-old, ranked No.74, had battled back from two sets down against Hubert Hurkacz when the distraught Pole quit with a left hip injury.
Struff won 3-6 6-7 (5-7) 7-6 (7-2) 7-5 4-2 to book his quarter-final berth.
