Tsitsipas moves on to the fourth round where he will meet Italian up-and-comer Jannik Sinner. The pair met in Melbourne last season, with Tsitsipas winning their quarter-final meeting on that occasion.
Popular with the fans, Tsitsipas enjoyed good support throughout his win.
"I enjoyed fighting my way through today," the Greek said in his on-court interview.
"It wasn't easy at times. I had the crowd with me, as always. It's always a great sensation when I'm out here."
Tsitsipas came through in the clutch to save a set point at 5-6 down and force a second set tiebreaker. He left the court happy with his game.
"I was good mixing it up today, mixing up my slice, opening the court," Tsitsipas added.
"I think my placement on serve was exceptional today. I didn't have a lot of rallies on my serve, which helped a lot today to keep things clean."
Already moving up one place to No 3 in the ATP Live Rankings this week despite having yet to match his semi-final effort from last term, Tsitsipas will leave as World No 1 if he wins his first Grand Slam title in Melbourne.
Meanwhile, over at the Margaret Court Arena, Jannik Sinner had fought back from the brink of elimination to defeat Marton Fucsovics for a place in the last 16.
Sinner completed his first career comeback from two sets down as he romped to a 4-6, 4-6, 6-1, 6-2, 6-0 win.
"For sure the first two sets were very tough for me," Sinner said before thanking the Margaret Court Arena crowd.
"Obviously I had to change something in my game after the two sets. I was feeling the ball quite well in the beginning, but the final shots I was missing a little bit. Tactically I was not so good."
Having fought back to 2-2 Sinner nearly slipped again when he dropped his opening service game of the final set.
However, he was able to immediately break back thanks to the faltering serve of Fucsovics.
The Hungarian lamented his failure to see out the win, admitting that Sinner forced him to alter his gameplan.
"The first two sets I think he was playing very well," Fucsovics said. "I went on court with one tactic and I had to change a little bit, obviously going a bit more to his backhand."
Tstitipas and Sinner are set to meet in their fourth round clash on Sunday.