Inspired seventh seed Rublev snatched the opening set but it was akin to poking a sleeping grizzly bear as Djokovic exacted painful punishment to stay on track for a fifth straight title.
Rublev played some brilliant tennis that would have accounted for pretty much any other player in the world.
But it was not enough to stop the Djokovic reaching his 46th Grand Slam semi-final, equalling the record of eight-time champion Roger Federer.
Second seed Djokovic will face Jannik Sinner (21) in the his 12th Wimbledon semi-final after the Italian also beat a Russian opponent in Roman Safiullin (25) earlier on Tuesday.
Asked afterwards how he copes with the pressure of being the player everyone wants to beat every time he steps on court, the Serbian said: "I love it, I'm serious. Pressure will never go away regardless of how many Grand Slams you win.
"Every time out here it awakens beautiful emotions and motivates me beyond anything I've dreamed of. I know they want to get the scalp, they want the win, but it ain't happening..."
DESTRUCTIVE FOREHAND
Boxing enthusiast Rublev boasts one of the most destructive forehands in tennis, often accompanied by a primal grunt that even Djokovic admits is 'scary'.
When Rublev broke serve in the eighth game courtesy of a couple of beefy forehands and held serve thanks to a Djokovic error to win the opening set it seemed a first win in a Grand Slam quarter-final at the eighth attempt was possible - even against a man without a Centre Court loss for a decade.
But Djokovic quickly reasserted his authority to race through a one-sided second set.
The Serbian was in control as he broke serve early in the third set but Rublev was not done and Djokovic was stretched to his elastic-limbed limits when serving at 5-4, fending off three break points and needing five set points in a sensational game to move within a set of his 33rd successive Wimbledon win.
Briefly deflated, Rublev fell 3-1 behind in the fourth set and there was no coming back as Djokovic wrapped up the win in his 400th Grand Slam match, a milestone reached only be Federer and Serena Williams.
"I feel like he's playing better and better compared to our matches before," Rublev said.
"Today was the first time I was ready to play, and I was there, I had these little chances that I didn't make. He made them. That's why he's Novak, one of the greatest in history."
