Musetti, a late replacement after the withdrawal of seven-times winner Novak Djokovic, began brightly but started to tire despite the backing of a largely partisan crowd at the Inalpi Arena, and Fritz proved unstoppable once his service game got going.
The turning point came in the third game when Fritz saved four break points, serving two aces in the process, and then broke Musetti to lead 3-1. The Italian, who won to love in his first service game, faced break points for the rest of the first set.
"I did a great job early on in the match to serve my way out of trouble and save some break points," Fritz said.
"I'm really happy. I thought I did a lot of things really well."
Musetti, beaten by Djokovic in an almost three-hour final in Athens on Saturday, managed to claw back four break points in the second set opener, but two double faults in his next service game gave Fritz the decisive break.
Serving masterclass
Fritz served nine aces in the second set, serving to love on three occasions, but the crowd roared back to life when Musetti took a 30-0 lead with the American serving for the match, only for Fritz to reply with two aces to wrap up an impressive win.
"The whole second set I played well and had a lot of chances to break that I didn't get," Fritz added.
"I'm really happy I was able to serve it out there and he didn't come back to ruin it."
Musetti's debut at the ATP Finals ended in defeat, but he managed to entertain the expectant Italian fans with some deft drop-shots to bring Fritz to the net and follow up with a lob to win the point.
The Italian also tried an underarm serve, which didn't come off, while Fritz dictated play from the baseline and continues his impressive form at the season-ending championships, having reached the semi-finals in 2022.
Top seed Carlos Alcaraz defeated Alex de Minaur 7-6(5), 6-2 on Sunday in the other Jimmy Connors Group game, and all four men in the group will play each other in a round-robin format, with the top two qualifying for the semi-finals.
The Italian fans will be back in force later on Monday when Jannik Sinner begins his title defence against Canadian Felix Auger-Aliassime in the Bjorn Borg Group.