The 21-time grand slam winner needed just over two hours to reach his 10th semi-final at the event – making him just the second player to hit double figures in the Open Era after Roger Federer (15).
Djokovic dominated from the off, breaking Rublev at just the second attempt and repeating the trick in the sixth game after angrily calling out a heckler between points.
Rublev faced seven break points in a one-sided opener as Djokovic pushed him back with a series of powerful groundstrokes, and there was to be little respite for the Russian in the second set.
Rublev gave up two breaks either side of a back-and-forth game in which Djokovic overcame intense pressure to hold, with the world number six ranting at the umpire over the time Djokovic took to serve.
Djokovic then held serve in another lengthy game to see out the second set, before securing another swift break at the outset of the third as a frustrated Rublev hurled his racquet to the ground.
While Rublev improved in a low-key third set, Djokovic's excellent service game ensured the Russian became just the second male player in the Open Era to lose each of his first seven major quarter-finals, after Tommy Robredo.
Djokovic, meanwhile, is in ominous form in his pursuit of a record-extending 10th Australian Open title, moving freely after being troubled by a hamstring injury in the earlier rounds, as he teed up a meeting with American Tommy Paul.