Playing in glorious sunshine after two days marked by wild swings in the weather, the highest-seeded man in the draw after the premature exits of holder Rafael Nadal and Casper Ruud played near-flawless tennis to the delight of Greek fans in the Rod Laver Arena.
"Fair crack of the whip mate, I mean, it was great," Tsitsipas said, slipping into the local vernacular. "I think my placement on the serve was exceptional today, I didn't have a lot of rallies on my serve, which helped a lot.
"Kind of kept things clean and I enjoyed the weather today, what a lovely day for tennis it is today, isn't it?"
Tsitsipas has not dropped a set in the tournament as he chases a maiden Grand Slam. But the 2021 French Open runner-up came close midway through the match, saving a set point in the second set before doubling his advantage following a tiebreak.
Roared on by Greek fans, many of them from Melbourne, which has the largest population of Greek speakers outside Greece and Cyprus, Tsitsipas eased through the next set without any drama to set up a tasty clash with 21-year-old Italian Jannik Sinner.
Sinner was made to work hard after a poor start to his match against Marton Fucsovics, dropping his serve twice and committing 18 unforced errors to lose the opening set, before eventually outlasting Fucsovics 4-6 4-6 6-1 6-2 6-0.
A neat passing shot at the net after powerful exchanges from the baseline helped Fucsovics break for a 2-1 lead in the second set and the world number 78 heaped more pressure on his opponent by going two sets up before Sinner switched gears.
The 15th seed, who has reached the quarter-finals of all four Grand Slams but has never gone any further, dropped only three games in the next three sets playing superior tennis against a fading Fucsovics.
Former French Open winner Barbora Krejcikova, a quarter-finalist at Melbourne Park in 2022, also went safely through with a 6-2 6-3 win over Anhelina Kalinina to set up a meeting with American third seed Jessica Pegula, who was also in a hurry to wrap up her match.
The third-seeded American swatted aside Marta Kostyuk 6-0 6-2 to make it seven straight victories in 2023 after a loss to Petra Kvitova in the United Cup.
Madison Keys looked like continuing her unbeaten start to the season when she took the first set against Victoria Azarenka only for the 2012 and 2013 Australian Open champion to rally for a 1-6 6-2 6-1 upset of the 10th seed.
Azarenka will next play world number 87 Zhu Lin of China, who stunned Greek sixth seed Maria Sakkari 7-6(3) 1-6 6-4 in the final match of the day.
No male U.S. player has captured a Grand Slam title since Andy Roddick at the 2003 U.S. Open, but the country's hopes have been rekindled with eight players in the third round.
Nadal's conqueror Mackenzie McDonald could not continue his run however, as the unseeded American fell to Japan's Yoshihito Nishioka who won 7-6(6) 6-3 6-2.
Frances Tiafoe and his eye-catching outfit also departed 6-3 6-4 3-6 7-6(9) at the hands of Russian Karen Khachanov in a meeting of the losing semi-finalists at last year's U.S. Open.
Sixth seed Felix Auger-Aliassime also advanced with a 6-1 3-6 6-1 6-4 win over Francisco Cerundolo, while fellow Canadian Denis Shapovalov came up short in a stirring comeback against 10th seed Hubert Hurkacz and bowed out 7-6(3) 6-4 1-6 4-6 6-3.
Cameron Norrie suffered a shock five-set defeat to Jiri Lehecka.
