The Australian No.1's backs-to-the-wall 7-6 (7-3) 6-3 win over the world No.6 Fritz means he will still make it into the semi-finals of the season-ending championship if Carlos Alcaraz beats Musetti in their group decider later on Thursday.
Such a scenario had looked wholly improbable after world No.7 de Minaur had been left completely dejected, losing after he'd served for the match against the weary but inspired home favourite Musetti on Tuesday at the Inalpi Arena.
He was the picture of misery at his post-match news conference, admitting that losing matches he felt he should have won was "getting to a point where mentally it's killing me". He added that if he didn't get it sorted, "it's going to eat me alive".
But on Thursday, with a sympathetic crowd right behind him, the 26-year-old Sydneysider showed magnificent resolve to earn the two-sets-to-zero victory that was his only chance of staying in the tournament.
It didn't come easy. He was locked at 4-4 and down 0-30 on his serve in the opening set, with the big-serving Fritz threatening to win the set which would condemn him to an early exit.
Instead, he rebounded in that game, went on to dominate with a brilliant tie break and then asserted his supremacy in a fairly one-sided second set to finally win an ATP Finals match at the sixth attempt, after having gone winless on his debut in Turin last year and then losing to Alcaraz and Musetti earlier this week.
After triumphing in an hour 34 minutes, de Minaur looked to the heavens and shook his hands in joy before going over to the courtside TV camera and scrawling "Finally" alongside a smiley emoji on the lens.
"I've dealt with a fair bit of heartbreak recently. It was good to - finally - get a win here in Turin," he explained afterwards.
"It means a lot. I mean, a couple days ago, I was in a pretty dark place, and it was a tough pill to swallow.
"So more than anything, I feel proud of my efforts, not for just coming out and winning, but also just for the mindset. I kind of make peace with it, and I just committed to my game from the first point to the last.
"I was gonna leave everything out there today and I ended up with a really good match from the start 'til the end. I've worked really hard, so it was good to get some positive reward for that hard work."
When told by his interviewer that he would make the last-four if Alcaraz beat Musetti, he said: "Is that actually true or not, I don't know. I don't trust you right now... I'm gonna have to see what happens.
"But, hey, ultimately, I kind of made my peace today, I was able to come onto the court with the mindset of not worrying about the 'what ifs?' and just focus on what I needed to do. And it's going to be a little bit more of that tonight.
"Whatever happens, happens, but I won't be paying too much attention to the tennis. I'll be relaxing and having a nice night here in Torino."
If the now-qualified Alcaraz beats Musetti, he will also be guaranteed the end-of-year world No.1 ranking, while if the Italian wins in front of his home fans, he will make the semi-finals at de Minaur's expense. Fritz's tournament, though, is over.
