The German 10th seed came back from one set down to beat Hungarian Fucsovics 4-6, 7-5, 6-4 in the round of 64 at Bercy Arena.
Zverev is still seeking to secure his place among the top eight who will go on to the ATP Finals in Turin next month.
After this victory, the 2021 champion sits seventh just behind Stefanos Tsitsipas and 430 points ahead of ninth-placed Hubert Hurkacz.
American Taylor Fritz's chances of qualifying for the tour's showpiece event took a hit when he was forced to retire with an abdominal injury.
On Monday, the ninth seed had comfortably beaten Argentine Sebastian Baez 6-1, 6-4.
The 11th-seeded Hurkacz saw off Sebastian Korda 6-3, 6-7(6), 6-3 on Tuesday to book his place in the second round alongside Felix Auger-Aliassime, who toppled Jan-Lennard Struff in two sets.
Later in the evening, world number two Carlos Alcaraz will take on Russian qualifier Roman Safiullin on centre court.
