
Cazaux, 21, raced into a 3-0 lead in the first set but was pegged back by ninth-seed Hurkacz, who came out on top in the tie-break on John Cain Arena.
There were no breaks in a serve-dominated second set but the 26-year-old Pole again won the tie-break to take a firm grip on the match.
He broke his 122nd-ranked opponent in the first game of the third set and never looked back.
Overall, Hurkacz won 91% of his first-serve points and was broken just once in the entire match.
The former Wimbledon semifinalist, whose previous best performance at Melbourne Park was the fourth round last year, will face third seed Daniil Medvedev in the quarterfinals.
“Arthur is such a great competitor, congratulations to him for an amazing run here,” said Hurkacz.
“I served well and he was serving well as well so I needed to stay aggressive and I’m really happy with today’s performance.
“I haven’t been into too many Grand Slam quarterfinals and super excited.”