It marked the 44th time that Djokovic reached the last four at the Grand Slams, leaving him six ahead of Rafael Nadal and only two behind his other great rival and 20-time major champion Roger Federer.
"I can't be happier with my tennis, I was solid from the back of the court. I love these conditions, this court, it's definitely special for me," Djokovic said.
Djokovic targeted Rublev's forehand and second serve with venomous returns in windy conditions on Rod Laver Arena and went ahead 3-1 in the first set after the Russian fifth seed double-faulted on break point and the Serb pulled away from there.
"You have to make adjustments and adapt," Djokovic said of playing in testing conditions. "It wasn't breezy at six in the evening and it started all of a sudden.
"People in the stands or watching on TV don't see it. But it makes a huge difference, as you have to pick and choose your shots and open up the court. The ball toss is a gamble.
"The scoreline in the opening two sets does not show the reality. Andrey's a great opponent, he has one of the biggest forehands. I knew the gameplan, but it's one thing to imagine and another to execute."
After taking the lead in the match with a brilliant backhand crosscourt winner, Djokovic showed how hard he is to beat on the grandest stage despite a strapped thigh due to a hamstring issue after the fourth seed broke in the fifth game of the second set.
He played exquisitely to save a break point in the next game and let out a huge roar before going on to double his advantage in the contest after a frustrated Rublev unloaded on his coach in the stands following another double fault.
Djokovic pounced early in the next set with Rublev appearing bereft of ideas and a seventh quarter-final defeat at a major looming, as the former number one closed out a convincing win on serve to set up a last-four meeting with American Tommy Paul.
"If I have to sum up the important shots, I found my best tennis," Djokovic said.
"Obviously he (Paul) doesn't have much to lose being in the semi-finals for the first time. He has been playing terrific tennis in the last 15 months.
"I have to be ready for the match mentally and not approach it differently. If I play this way, I have a good chance to go through."
