The Serbian was in the zone to blitz past the Russian 6-1, 6-2, 6-4 on Rod Laver Arena and meets Tommy Paul for a place in Sunday's final.
The unseeded American Paul defeated countryman Ben Shelton 7-6 (8/6), 6-3, 5-7, 6-4.
"I cannot be happier with my tennis, honestly," said Djokovic, after reaching a 10th semi-final at Melbourne Park. Only Roger Federer (15) and Jack Crawford (11) have been there more often.
"I've been playing very solid from the back of the court and I really love playing in these conditions and this court," the 35-year-old told Rod Laver Arena.
"Some really close games that we had," he added. "Andrey is a great opponent, great player. I have tons of respect for him, one of the biggest forehands, quickest players on the tour.
"I knew what the game plan was and it was important that I found my best tennis."
Djokovic's quest for a record-extending 10th Australian Open title has been far from smooth, plagued by a left hamstring strain suffered en route to the title at Adelaide this month.
He struggled physically in the early rounds but was dominant during his fourth-round demolition of Alex de Minaur, and he showed few problems against Rublev.
Victory for the red-hot favourite propelled him into a 44th Grand Slam semi-final to close the gap on Federer's all-time record of 46.
In another astonishing record, he clocked a 26th consecutive match-win at the Australian Open to equal Andre Agassi's Open-era record for longest streak at the first Grand Slam of the year.
The signs were ominous for Rublev before the match even started.
In contrast to Djokovic's outstanding record in Melbourne, Rublev -- who was taken to five sets by Holger Rune in the fourth round -- came into the clash with a 0-6 record in Grand Slam quarter-finals.
After a shaky start when he served double fault to open proceedings, Djokovic quickly settled into a rhythm.
The Russian, who also sent down a double fault to start, struggled early on.
His serving jitters persisted and when the Serb worked a break point at 2-1 he double-faulted again in response.
Djokovic was on fire and raced to a 4-1 lead before converting a fifth break point to speed 5-1 clear and clinch the set in 39 minutes.
Rublev had no answers to his precision and power.
Djokovic continued in the same vein in the second set, grabbing his opportunity in game four after a 16-shot rally when Rublev blinked first with a backhand error.
Another break left Rublev frustrated and castigating himself as he slumped two sets down.
He took a bathroom break in between sets, but it didn't work as Djokovic came out with more venomous shots and broke his serve in the opening game and never let up.