The 24-time Grand Slam champion, who turns 38 on Thursday, is playing in Switzerland to gain some extra match time ahead of the start of the French Open this weekend.
Djokovic eased to a 6-2, 6-3 win over Hungarian Fucsovics to set up a quarter-final on Thursday against Matteo Arnaldi.
Italian Arnaldi dumped Djokovic out in his opening match at the Madrid Masters last month, after the Serb also lost his opener in Monte Carlo to Alejandro Tabilo.
Djokovic, who is sixth in the ATP rankings, did not face a single break point in a dominant win over world number 134 Fucsovics.
It was his first match since splitting from coach and former rival Andy Murray last week.
American top seed Taylor Fritz also booked a last-eight place, beating Frenchman Quentin Halys 6-4, 7-6 (7/5). (AFP)
