The Greek third seed showed grit to defeat Russia's Khachanov and set up a final against either nine-time Melbourne champion Novak Djokovic or American Tommy Paul.
The 18th-seeded Khachanov threatened a comeback after saving two match points to force the semi-final into a fourth set, before Tsitsipas triumphed 7-6 (7/2), 6-4, 6-7 (6/8), 6-3.
Tsitsipas can top the world rankings if he wins his first Grand Slam crown on Sunday.
"I dreamed as a kid to maybe one day get to play in this court against the best players in the world," said Tsitsipas, who is now 10-0 for the season and on the brink of a first Grand Slam crown.
"So I'm happy with the fight I put out there today. I feel blessed, blessed that I'm able to play tennis at this level. I've been wanting for many years now to put Greek tennis on the map.
"I'm extremely happy that I'm in the final now and let's see what happens," he added.
At 24, Tsitsipas is the youngest man to reach the Australian Open final since a 23-year-old Djokovic in 2011.
Tsitsipas has thrived in Melbourne throughout his career after bursting on the scene at the 2019 event as a 20-year-old when he dethroned defending champion Roger Federer in the last 16.
He went on to reach the semi-finals that year and again in 2021 and 2022 - falling one match short on each occasion - to highlight the consistency that has made him a mainstay of the world's top 10 for nearly four years.
A Grand Slam crown has remained elusive, with his runner-up showing at Roland Garros in 2021 his best result so far, falling to Djokovic in five sets after holding a 2-0 lead.
'Couldn't be more ready'
A confident Tsitsipas opened with a serve to love and applied early pressure, earning a break in game four when US Open semi-finalist Khachanov made a baseline error.
But the advantage didn't last, with the 26-year-old Russian immediately striking back to level it up when Tsitsipas netted a forehand.
The Greek star was unrelenting on the forehand and forced another break for a 5-3 lead, only for Khachanov to again roar back.
It went to a tiebreak, with Tsitsipas quickly wrapping it up.
Khachanov repelled three break points early in a second set which went with serve until Tsitsipas earned another two after a 22-shot rally at 4-4, and this time he made no mistake.
With the bit between his teeth, the world number four ramped up the pressure to secure a break for 2-1 in the third set, then consolidated.
Khachanov looked down and out but in a late twist broke back when Tsitsipas - two points from victory - sent an overhead volley wide as he served for the match.
It propelled the third set to another tiebreak, where the Greek worked two match points on serve, but failed to convert and the Russian pulled out of the mire to drag it to a fourth set.
Tsitsipas quickly snuffed out any chance of a comeback as he reasserted his dominance to seal a spot in the final.
Afterwards, Tsitsipas struck a confident tone - no matter who he meets in the final.
"Couldn't be more ready for this moment," said the Greek, who has enjoyed strong support from Melbourne's large Greek population.
"I'm playing great tennis. I'm enjoying myself. I just see no downside or negativity in what I'm trying to do out there," he added.
