Norrie, who was once again the last British singles player standing at a grand slam, was looking to follow up his run to the Wimbledon semi-finals but was below his best in a 6-4 6-4 6-4 loss.
The 27-year-old will now turn his thoughts to leading Britain’s Davis Cup team in Glasgow next week while Rublev moves forward to a sixth slam quarter-final against either Rafael Nadal or Frances Tiafoe.
This was a third meeting between the pair, with Rublev winning their first match in 2020 but Norrie coming out on top in San Diego last year.
Both men play at tennis’ coalface, relying on grit, athleticism and competitive desire as much as serves, forehands and backhands.
Norrie had vowed to play with an aggressive mindset against ninth seed Rublev, who likes to play on the front foot, and he certainly went after his forehand in the opening few games.
Inevitably that meant more errors but it was Norrie’s backhand, usually his most reliable shot, that let him down as he was broken in the ninth game of the opening set.
It was the same story early in the second set, with Rublev breaking again in the third game, and, when Norrie created his first chance in the next game, the Russian saved it well.
Humidity levels were high and the sky was darkening but officials delayed closing the roof on Louis Armstrong Stadium as heavy spits began to fall, meaning a lengthy break while the court was dried.
That did not change the momentum, though, as Rublev served out the second set to put himself firmly in control.
One of Norrie’s two successful recoveries from two sets to love down came here two years ago against Diego Schwartzman in what remains the best victory by ranking of his career at a grand slam.
This would have surpassed it – an indication of how sudden Norrie’s elevation to the top of the game has been – but that never looked on the cards.
Another forehand error gave Rublev a break for 3-2 in the third set and Norrie’s frustration came out in the next game when he slammed his racket to the court, earning a warning.
Fired up, Norrie played some of his best tennis of the match to break back and now it was Rublev, who is always quick to berate himself, losing his cool.
But Norrie came under pressure again at 4-4 and a final backhand error from the seventh seed sealed his fate.