The Demon won the first set and then dropped the second, but regathered himself to comfortably win the next two for a 6-2, 5-7, 6-2, 6-4 win in just over two-and-a-half hours.
It continues a strong run up the world rankings for Svajda, who also made the round of 16 at Roland-Garros. De Minaur is three wins from three appearances on Court 3 at the All-England club.
“This almost feels like an Aussie court … the atmosphere has been unbelievable,” he said in his courtside interview, before piling a heap of praise for his opponent.
“I thought he was a hell of a player (and) it’s not a one-time thing – he made fourth round at Roland-Garros,” De Minaur said.
“Then here he’s playing some incredible tennis. I expect him to rise up the rankings very, very quickly. I just wanted to wish him all the best because he’s a hell of a talent.
“I hadn’t played him before, and I think he’s quite awkward. He’s he plays some great tennis from both sides. He’s got one of the best running forehands I think I’ve ever seen in my life.
“He’s so loose, and he looks like he’s barely using any energy. And he’s got such great timing of the ball.
“That second set, I played really, really well to hang in there, but he was just too good.
“I was just happy to kind of maintain my level throughout the whole match. I was ready for a battle, and luckily, it went my way.”
Demon stunned in the third set with a brilliant dive that sent the crowd wild.
Svajda unleashed a massive forehand that for all money looked like a winner, only for De Minaur to dive full length to his right to get the ball back over the net. Not only did he succeed, but he had time to get back to his feet and hit a volley winner from the return.