The eighth seed put on an impressive display on Court Suzanne Lenglen as he powered to a 6-2 6-3 3-6 6-3 victory.
Ruud became the first player at this year's French Open to win a set against Hurkacz as the Pole's usually reliable first serve appeared to elude him.
The Norwegian won the first two sets before Hurkacz began to make in-roads and even threatened a comeback.
However, Ruud was able to regain composure in the fourth and went on to complete the fourth round victory in two hours and 31 minutes.
After the match, the 23-year-old said: "It's been one of the goals for me this year, to try and reach the quarter-finals of a Grand Slam.
"I don't know why, but suddenly when I came here this year I felt a little bit more experienced playing five sets. I wasn't able to play in Australia so Roland Garros was a big goal for me, especially this year."
Ruud has been one of the most consistent clay players on the ATP tour in recent years, having picked up seven of his eight titles on the surface.
Until this year, the Norwegian star was unable to make it past the third round at Roland Garros, falling at this stage in 2019, 2020 and 2021.
He added: "Hubert has improved a lot on clay from previous years. He has become a dangerous player on all surfaces, especially here on the clay where if the sun is out, it is quite fast.
"Of course, he has a dangerous serve, and the goal today was to try and get many returns back. I did very well in the first two sets. I was able to make him play a lot of points and was able to run around my forehand and control many points.
"He raised his level a little bit in the third, and one poor service game by myself and then he had a break.
"It turns around quick in tennis. It was looking a bit dark in the fourth set as well but luckily I was able to break him back a couple of times."