De Minaur lived up to his 'Demon' nickname, showing energy and character as he hustled the lethargic-looking American all over the court, and after taking the first-set tiebreak, stormed to victory following an early break in the second set.
A victory for Spanish world number one Alcaraz against Musetti in the other Jimmy Connors Group match would send De Minaur into the semi-finals along with Alcaraz, but a Musetti win would see the Australian exit the season-ending championships.
"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," De Minaur said when told of the permutations.
Alcaraz is now assured of his place in the semi-finals, win or lose, though defeat would put him in second place in the group, while a win would guarantee the Spaniard the year-end world number one spot ahead of Italy's Jannik Sinner.
Last year's losing finalist Fritz, who beat Musetti in his opener before losing a thrilling three-setter against Alcaraz, struggled with his normally reliable serve, and was put to the sword by the Australian, desperate for his first ATP Finals win.
De Minaur, who lost all three round-robin matches on his debut last year, was beaten by Alcaraz and then suffered a devastating defeat to Musetti having held a 5-3 lead in the final set.
"I have dealt with a fair bit of heartbreak recently, so it was good to finally get a win here in Turin," De Minaur said.
The Australian bounced back from that loss which had left him in a dark place, while Fritz appeared heavy-footed as he lacked the pace required to deal with De Minaur's dynamism.
De Minaur broke to lead 3-1 in the first set, and while Fritz rallied to force a tiebreak, the Australian dominated it, racing into a 4-1 lead with two mini-breaks. He began the second set in a similar vein where he broke to love and went 3-0 up.
This time there was no comeback from Fritz. He managed to save a break point at 2-5 down but De Minaur served out for the win, and after looking down and out after the Musetti match, the Australian gave himself a real chance of advancing.