The victory moved Djokovic 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.
Also in pursuit of a standalone 25th Grand Slam trophy, the 39-year-old Djokovic has steadily gained momentum on the famous lawns of southwest London and heads into the last eight having again shown his knack for navigating danger.
"Another hard-fought win," Djokovic said. "Roman started very well and very aggressively. I didn't feel as comfortable from back on the court.
"I knew it was going to be a challenge, staying in the rally with him, particularly from the end where you played against the wind pretty much the whole match. He's just a very solid player, and I respect him a lot."
It was far from smooth sailing for the seventh seed 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 number 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.
"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," Djokovic added.
"I had to mix things up, and it worked in some moments and didn't in some. But in the end, I found the accuracy really and precision with the first serve. That really got me out of trouble in the fourth set."
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.
"Survive to thrive," Djokovic said as he reflected on his first week during which he has dropped sets in three of his first four matches. "That's how I feel. Hopefully the thriving part is coming."