The Italian came into the Labour Day evening clash at Arthur Ashe Stadium looking for his 25th straight major match win on his preferred surface and he never looked in any trouble against a tricky opponent after shooting out of the blocks.
"He (Bublik) had a tough match last time, finishing late. He didn't serve as well as he does. I broke him in every set and it gave me the confidence to play well," the top seed said.
"My first night session match, it makes such a difference. Thanks everyone for coming, this is such a special occasion for us players."
Sinner built a 4-0 lead before the Kazakh could even get on the board and the dominant 24-year-old chased down a drop shot to fire home a backhand winner that wrapped up the opening set.
Bublik's attempts to disrupt Sinner's rhythm with more drop shots proved futile but it was his service errors that left him trailing by two sets, before Sinner wheeled away to his eighth straight major quarter-final and a clash with compatriot Lorenzo Musetti.
Musetti, the 10th seed, earlier booked his last-eight place with a comfortable dismissal of Jaume Munar, 6-3 6-0 6-1.
Elsewhere, Felix Auger-Aliassime sealed a meeting with Australian No.1 Alex de Minaur with a composed 7-5 6-3 6-4 win over Andrey Rublev.
The 25-year-old, reaching his first major quarter-final since the 2022 Australian Open, kept his cool to notch his second victory in nine meetings with the Russian.
The Canadian admitted the moment carried extra weight after battling injuries and dips in confidence since his 2021 breakthrough semi-final run at Flushing Meadows.
"Today is my first time playing Arthur Ashe in a few years. It feels even better than the first time," Auger-Aliassime said.
"In '21 I was on my way back and had a few setbacks and injuries, struggles with confidence. To come back here for the second time, it feels better and more deserved. I'm soaking in every moment here."
The 25th seed, coming off a stunning win over world No.3 Alexander Zverev, credited his mental approach for back-to-back statement victories.
"It is always a battle and it was important for me to stay ahead and keep putting pressure on to the last point," he said.
"In those tight moments, you want to come with the right state of mind. There's a lot of excitement around in our world today but on the court we need to be calm-headed in those big pressure moments."
Rublev, having simmered for a long time, smashed his racquet on the court after losing the second set.
