Tsitsipas pleased with passion in straightforward Australian Open win
The Greek seventh seed dropped the first set in both of his opening two matches but managed to avoid the same fate against France's Luca Van Assche on Rod Laver Arena, cruising home 6-3, 6-0, 6-4.
It lined him up with a tough clash next with American 12th seed Taylor Fritz, who ground past Hungary's Fabian Marozsan 3-6, 6-4, 6-2, 6-2.
"I had a little bit more experience under my belt today and I am delighted with the win. It means a lot to me," said Tsitsipas, who made the final last year, losing to Novak Djokovic.
"I felt like I had a poor start in both (previous) matches and felt like I wanted something different this time. It's not easy always having to fight back and show your best tennis in the second set.
"I wanted to go out here today and show that passion and determination from the very beginning and I'm happy that things worked out.
"I was constantly trying to push myself and exceed my own expectations. I'm happy things worked out and it went smoothly after the first set."