Ruud was sharp at the outset, breaking for a 5-3 lead before grabbing the first set with a love hold.
But the American began to make inroads against Ruud's serve in the second and finally converted a break when the Norwegian, who had been using a towel to wipe up his own sweat from the court on a humid day in New York, double-faulted on set point to level the match.
Ruud changed into dry clothes and shoes before the third but never regained his form.
He produced a horrendous service game that ended with him dumping a backhand into the net to fall 2-0 behind in the third and Fritz, seeded 12th, captured the set with an ace.
Fritz kept his foot on the gas in the fourth, hammering his 24th ace on match point to set up a quarter-final meeting with either fellow American Brandon Nakashima or German fourth seed Alexander Zverev.
"I just had to stay in it. He definitely outplayed me in the first set," Fritz said in an on-court interview.
"I did a really good job to fight in the beginning of the second and apply some scoreboard pressure.
"And then I felt his level dropped a little bit and it became a bit more playable for me. I was getting more looks at second serves and I was able to just get through it from there."
The victory is the first for Fritz in three meetings against Ruud, who came out on the winning side of a tight three-setter at the ATP Finals in 2022 and at the French Open this year.
"I didn't think too much about the head-to-head before the match," Fritz said.
"One meeting was 7-6 in the third, the next was this year at the French and he's pretty good on clay, so I didn’t think too much about that. I just did a really good job to stay with it."
Last year Fritz fell in straight sets to eventual champion Novak Djokovic in the quarters but will not have to face the Serbian 24-time Grand Slam champion this year after he was upset in the third round.
With Djokovic and third seed Carlos Alcaraz out of the draw, it would be tempting for Fritz to fantasize about lifting his first Grand Slam trophy but said he has learned the hard way not to get too far ahead of himself.
"I came into the tournament in 2022 saying I thought I could win it and I lost in the first round," he said with a smile.
"So I think it's good to just take it one match at a time and focus on the person in front of you."