Tsitsipas was a convincing 6-3, 7-6 (7/2), 6-4 winner over unseeded Jiri Lehecka of the Czech Republic and faces Karen Khachanov next.
The 24-year-old Tsitsipas is the highest remaining seed left at three and with Melbourne's large Greek community roaring him on, his title charge is gathering pace.
"It felt different this time from any other match and the most important thing in the end is that I found a solution," said Tsitsipas, after making the Australian semi-finals for a fourth time.
"It was a very difficult three-setter, one of the most difficult so far in the competition," said the Greek, who will become world number one should he win the title.
The other quarter-final at Rod Laver Arena between Russia's Khachanov and Sebastian Korda had been warming up nicely until the American hurt his wrist.
The 18th seed went through when Korda retired in the third set, down 7-6 (7/5), 6-3, 3-0.
The 22-year-old Korda, who had been attempting to emulate his father Petr's Australian Open victory in 1998, said afterwards that he could barely hold the racquet.
He said he first felt the injury while playing the Adelaide International this month, where he made the final and forced a championship point before being beaten by Novak Djokovic.
But it had not bothered him in the opening four rounds at Melbourne Park until he hit a return in the second set.
"Volleying was almost impossible for me, so it was a little tough."
For Khachanov it is a second consecutive Grand Slam semi-final, having reached the last four at the 2022 US Open.
Nine-time Melbourne champion Djokovic is still on the scene, with a quarter-final against Russian fifth seed Andrey Rublev on Wednesday.
The other quarter-final is an all-American clash between Ben Shelton and Tommy Paul.
'It's my weapon'
Azarenka is back in the last four in Melbourne for the first time since she won the tournament in 2013 and will face big-serving Elena Rybakina.
The Belarusian Azarenka, who also triumphed in 2012, secured an impressive straight-sets victory over Jessica Pegula.
Third seed Pegula was hotly tipped to win the title but the American simply had no answers to Azarenka's pounding forehand groundstrokes.
The 33-year-old Azarenka rolled back the years in a surprisingly one-sided quarter-final to triumph 6-4, 6-1.
"Well, it hurts to beat her because I always want her to do well," the 24th seed said of Pegula, a close friend and practice partner.
Asked how her young son Leo would receive his mum's latest achievement, Azarenka said: "He's more worried about his football and when we're going to play again.
"He definitely wants his mum to be home."
Leo will have to wait at least a few more days because Azarenka faces Moscow-born Kazakh Rybakina on Thursday for a place in the final.
Rybakina blasted her way into the semi-finals with a ruthless 6-2, 6-4 win over Jelena Ostapenko.
The 23-year-old Rybakina sent down 11 aces to blow former French Open champion Ostapenko off court in 79 minutes.
The 22nd seed has blasted 35 aces so far, more than any other woman at the tournament.
Ominously, she said her serve is better now than when she won Wimbledon last year.
"I gained even more power. It's my weapon on the court and of course we are trying to work on it," she said.