The 27-year-old Australian was more consistent than the world number 99 Frenchman, who struggled with blustery conditions and produced an error-strewn performance.
De Minaur will face French left-hander Adrian Mannarino in the semi-final, after the world number 46 ended a surprise run by Chinese outsider Zhizhen Zhang.
"I got lucky with a couple of net cords at the end but I'm super pleased with the performance and happy to stay here a but longer," said the Australian.
"I would be very happy if I could maintain this level," he added.
The second-seeded de Minaur powered through the first set in just 24 minutes, breaking Bonzi in his second service game, helped by a lucky net cord.
A double-fault by the Frenchman handed de Minaur an insurance break, and he wrapped up the first set 6-2 courtesy of a forehand error from Bonzi.
De Minaur faced his own break point in the fifth game of the second set but saved it with an exquisite backhand volley drop shot and went on to clinch the game.
The second set went on serve until the seventh, when de Minaur again benefitted from a lucky cord before unleashing a blistering forehand drive up the line to break and take a strangehold on the match.
The Australian wrapped up the match in just over an hour, sealing the second set 6-4 with a service winner.
De Minaur, who lifted the title in 2024 on the grass at 's-Hertogenbosch, is seeded to face Felix Auger-Aliassime in the final, with the Canadian now at his career-high world ranking of four.
The 25-year-old Auger-Aliassime, making his first appearance at the tournament, faces Kamil Majchrzak, the world number 76 from Poland later Friday.
Earlier, Russian Daniil Medvedev came through a three-set thriller against Dutch 17-year-old Thijs Boogaard 3-6, 6-4, 7-6 (8/6) after saving a match point.