On a hot and humid afternoon, the world number four seemed lethargic and struggled to get into his stride, unnerved after Mpetshi Perricard nearly broke twice in the fifth game.
That preempted a streak of brilliance that saw the neon orange-clad Frenchman fire three aces to hold the sixth, then break in the seventh.
A closely fought second set came to a head in the 11th game when a double fault by Fritz handed Mpetshi Perricard the advantage, which he swiftly converted with a backhand.
Finishing the match off with two aces, the big-serving 22-year-old said he had learnt a lot during the match.
"I'm really happy to get the win," he said, still catching his breath.
Denmark's Holger Rune, ranked 11th in the world, beat France's Ugo Humbert, 6-4, 6-4.