The Greek third seed triumphed 7-6 (7/2), 6-4, 6-7 (6/8), 6-3 under hot sun on Rod Laver Arena to set up a final against either nine-time champion Novak Djokovic or American Tommy Paul.
At 24, he is the youngest man to reach the final since a 23-year-old Djokovic in 2011.
If either he or the Serbian great lift the trophy, they will become world number one.
"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.
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.
But a Grand Slam crown remains 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.
Tsitsipas came into the Khachanov clash brimming with confidence, further fuelled by enjoying a 5-0 record over the Russian.
He opened with a serve to love and applied early pressure, earning a break in game four when Khachanov made a baseline error.
But the advantage didn't last with the 18th seed immediately striking back to level it up when Tsitsipas netted a forehand.
The Greek star, though, 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 taking charge.
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 third seed 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 through to take drag it to a fourth.
Tsitsipas, whose mantra in Melbourne has been to focus on the positives not the negatives, kept his cool and plugged away to break again for 2-0, and this time there was no comeback.