Serbia’s Djokovic, 35, cut a frustrated figure at times but channelled his emotions into a ruthless 6-1 6-2 6-4 win over Russia’s Rublev in Melbourne.
The fourth seed, who again had his left thigh strapped, will play American Tommy Paul in the last four on Friday.Paul, 25, ended Ben Shelton’s surprise run to reach a first major semi-final.
American world number 35 Paul won 7-6 (8-6) 6-3 5-7 6-4 against 20-year-old compatriot Shelton on Rod Laver Arena.Greek third seed Stefanos Tsitsipas will meet Russian Karen Khachanov in Friday’s other semi-final.
Former world number one Djokovic, who was the only major champion in the men’s quarter-finals, is favourite for the title as he chases a record-equalling 22nd Grand Slam.
Beating Rublev was his 26th consecutive win at Melbourne Park, equalling the Open-era streak recorded by American Andre Agassi.”I could not be happier with my tennis. I’m playing solidly from the back of the court and love these conditions,” said Djokovic, who has not been practising on the days between matches.
“I’m going to keep going. I think it’s important to be smart and wise with the body in these circumstances where it’s more important to recover and get ready for the next challenge.”
Djokovic looked close to his best in a dominant win over Alex de Minaur in the fourth round, but the way he demolished an opponent of higher pedigree in Rublev was even more impressive.
Much of the talk has centred around the scale of Djokovic’s hamstring injury, and racing through another victory – this one in little more than two hours – seems to be the best way to protect the problem.
Rublev has one of the most powerful forehands in the game, but was dispirited by Djokovic’s precise and incessant returning.
Asked if it was his best performance of the tournament, Djokovic said: “I would rank it as number two but it is very close to the performance of two nights ago [against De Minaur].
“Overall, the scoreline in the first two sets doesn’t tell the truth of the close games we had.”If I have to sum it up, in all the important moments I played the right shots and the right tennis – that’s what pleases me the most.”
After saving a break point in his first service game, Rublev miscued a forehand to bring up another in the next and meekly handed it over with a double fault as Djokovic moved 3-1 ahead.
Djokovic was annoyed by a heckler during the sixth game but it did not disrupt his rhythm as he took Rublev’s serve again for 5-1, allowing him to serve out the opening set but only after seeing off two break points.
Despite playing superbly and being in command, Djokovic did not look completely happy and had a frank exchange with coach Goran Ivanisevic early in the second set.
Whatever was said worked, Djokovic winning the next seven points to move a break ahead and take control again.
A ferocious roar came when he fought off two break points for 4-2, and Rublev’s own annoyance was audible when he was broken in the next game.
Rublev had lost all six of his previous major quarter-finals, and facing Djokovic as he aimed to end that run was the last thing he wanted.
The Russian joked after his last-16 win that he wished he was in the opposite side of the draw to Djokovic – but it was no laughing matter as he became increasingly despondent on the way to losing the second set.
His mood became more forlorn as he was broken in the first game of the third, and Djokovic was not threatened as he served out victory to reach his 10th semi-final at Melbourne Park.