Rublev looked up to the task from the start and proved to be unflappable against Kyrgios, who complained to his team in the box several times about not being able to see and later said he took time adjusting to the massive Arthur Ashe Stadium.
The Australian seemed to have no issues with his vision on serve, however, at one point firing four consecutive aces in a 40-second game to force a first-set tiebreak. He saved two set points before sending a backhand just wide to lose the opener.
Kyrgios got his only two break point chances while leading 3-2 in the second set but Rublev beat them both back.
The pair remained on serve to bring up another tiebreak and while Kyrgios jumped out to a 4-0 lead a determined Rublev took seven of the next eight points to snatch the set and grab control of the match.
"I had chances. I just didn't take them," said Kyrgios. "Nowhere near my best tennis, but it is what it is."
The final set was on serve until Rublev got the only break of the match and immediately consolidated for a 5-2 lead that sent him on his way.
Kyrgios lost despite powering down 30 aces to Rublev's 12 and winning almost 90 per cent of his first-serve points while saving three of the four break points he faced.
"His serve is the best on tour. I was just trying to focus on me to serve also well to keep my serve and see if I win tie-breaks or not," said Rublev. "Today was my day and I am happy."
Rublev came into the year's final Grand Slam with plenty of confidence after he earned the biggest win of his career when he beat Roger Federer in the third round at Cincinnati.
After making headlines this week for both his comments and on-court behaviour, Kyrgios avoided controversy on Saturday but did shout "whistleblower" in the direction of a line judge who had gone to the chair umpire to report foul language.
Rublev, who reached the New York quarter-final two years ago, will face Italian Matteo Berrettini in the fourth round on Monday.
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