The Serbian superstar came through a probing test on Rod Laver Arena against 12th seeded American 7-6 (7/3), 4-6, 6-2, 6-3 to keep his bid for a 25th major crown on track.
Djokovic almost always gets the evening slot on centre court, but was bumped to the afternoon on a day where temperatures soared to 32 degrees Celsius (90 degrees Fahrenheit) and the world number one admitted it was hard going.
"Physically and emotionally very draining," he said after the three hour and 45 minute slog, adding that he "suffered a lot" in the first two sets.
"He was serving well, staying close to the line and kind of suffocating me from the back of the court," he said.
"I think I upped my game probably midway through the third set all the way to the end."
The 36-year-old will face either Italian fourth seed Jannik Sinner or Russian fifth seed Andrey Rublev next, with the omens not good for either man.
Djokovic has won all 10 previous semi-finals he has played at Melbourne Park, stretching back to his first title in 2008.
Error-strewn US Open champion Gauff was also put through her paces before outlasting unseeded Ukrainian Marta Kostyuk after more than three scrappy hours 7-6 (8/6), 6-7 (3/7), 6-2.
She will meet either power-packing defending champion Aryna Sabalenka or ninth-seeded Barbora Krejcikova for a place in the final.
But her performance will not strike fear into whoever she plays next, with the 19-year-old struggling on serve and wasting countless opportunities.
She admitted it was below-par, giving herself only a 'C' rating.
"Hopefully got the bad match out of the way and I can play even better," she said.
The low standard was not confined to Gauff, with the pair making a staggering 107 unforced errors between them -- there were 16 service breaks.
Kostyuk rued missing her chances, letting slip a 5-1 lead and squandering set points in the first set, but said she was proud of how she fought.
"Very proud of myself. I won for myself today, and I think it's the most important thing," said the 21-year-old, who has been vocal at the tournament about keeping people's focus on the conflict in her homeland.
Gauff also faltered at crunch moments, broken when serving for the match at 5-4 in the second set before keeping her cool as Kostyuk became more agitated in the deciding set.
It extended her winning streak this year to 10 matches after she won at Auckland in the lead up, and her unbeaten run at Grand Slams to 12 after her title-winning exploits at Flushing Meadow.
"Really proud of the fight I showed today," said the American, who had never progressed beyond the fourth round at Melbourne Park in four previous attempts.
"I really fought and left it all on the court."
She will need to step up a level should she face Sabalenka, who has been ruthless so far in Melbourne, conceding just 11 games in her march towards another title.
But the Belarusian world number two is expecting a thorough examination from Krejcikova, the 2021 French Open champion, who is yet to go beyond the last eight at Melbourne Park.
"Barbora, we played a lot of matches. She plays really well. I think she's coming back after injuries, so also super-motivated. Always a tough battle," she said.