The 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 tie-break.
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 and set up a quarter-final clash with either third seed Felix Auger-Aliassime or Spaniard Alejandro Davidovich Fokina.
"Another hard-fought win. Roman [Safiullin] started very well. He was very aggressive so I didn't maybe feel as comfortable from the back of the court," Djokovic added.
"I haven't felt inferior from 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."
