Tsitsipas, who had crashed three times at the semi-final stage at Melbourne Park, will take on favourite Novak Djokovic or Tommy Paul for the title, reports Reuters.
Winning his first Grand Slam crown on Sunday would see Tsitsipas take the number one spot from Spain’s Carlos Alcaraz, who is absent from the tournament due to injury.
“I’d like that number,” Tsitsipas said. “These are the moments that I have been working hard for, to be able to play in finals like this, but finals that have a bigger meaning than just the final. So it’s a cornerstone final.
“I’m fighting for the number one spot. It’s a childhood dream to be capturing the number one spot one day, I’m close.”
Playing in glorious sunshine on Rod Laver Arena, the 2021 French Open runner-up forced an error on the Khachanov forehand to grab an early break only to immediately surrender his serve.
The pair traded breaks again in a see-sawing opening set but Tsitsipas came alive in the tiebreak and went ahead in the match before getting his nose in front in the second set when his opponent’s level dropped.
Despite being rattled by three foot faults and two time violations on serve, Tsitsipas looked more comfortable after wining the second set.
The 24-year-old broke Khachanov for a 2-1 lead in the third but the Russian showed great courage to fight back and draw level at 5-5 before it went to a tiebreak.
Tsitsipas hit two superb inside-out forehands to draw roars from his many supporters in the crowd, but squandered two match points and allowed Khachanov to take the set.
Tsitsipas regrouped in the fourth set to go 3-0 up and went on to close out the match in style and claim a place in his second Grand Slam final.
“I’ve been wanting for many years now to put Greek tennis on the map, and me and Maria (Sakkari) have done an incredible job,” Tsitsipas said.
“I know it probably doesn’t mean as much for Australians because they’ve been always producing players and they’ve always had their fair share of top players but coming from a small country like Greece I’m so grateful I get some more like this.”
DISTRACTION FOR DJOKOVIC
Looking to join him in the final is Djokovic, who is bidding for a record-extending 10th Australian Open title and 22nd Grand Slam to equal Rafa Nadal, but the Serbian great will not have his father in the stands in the evening semi-final.
Srdjan Djokovic said he would not attend his son’s match and would instead “watch from home” after a video emerged showing him posing at Melbourne Park with fans holding Russian flags on Wednesday.
Russian and Belarusian athletes can compete as individual athletes without national affiliation at the tournament, though their flags are banned from the grounds after a complaint by Ukraine’s ambassador last week.
The video caused controversy in Australia, leading to the country’s Prime Minister Anthony Albanese reiterating Australian support for Ukraine and criticising supporters of Russia’s invasion, which Moscow calls a “special military operation”.
Srdjan Djokovic said he did not want to be a distraction.
“I am here to support my son only,” he said in an emailed statement. “I had no intention of causing such headlines or disruption.
“So there is no disruption to tonight’s semi-final for my son or for the other player, I have chosen to watch from home.”
Earlier on Friday, Brazilian pair Luisa Stefani and Rafael Matos beat India’s Sania Mirza and Rohan Bopanna 7-6(2) 6-2 to win the mixed doubles final, with the result marking the end of Mirza’s Grand Slam career.
“I’ve had the privilege to come back here again and again, and win tournaments and play some great finals,” an emotional Mirza said.
“Rod Laver Arena has been special in my life and I couldn’t think of a better arena to finish my career at a Grand Slam.”