The German, who ousted 14-times champion Rafael Nadal in the opening round, had to work hard to win the first-set tiebreak but broke early in the second.
Former quarter-finalist Goffin nearly broke Zverev's serve in the fourth game but the German held firm, mixing up his game well to close out the match.
"I was happy that I ran away with it but also happy that I played well," said Zverev, who suffered a season-ending ankle injury in the 2022 French Open semis.
The two men had already met five times before at tour level, including four times on clay, with Zverev leading by three wins to two.
Former world number seven Goffin said the contest was tough with the German firing down serves and playing well from the baseline.
Zverev, who is now on an eight-match winning streak after claiming the Rome title, will next face Italian Luciano Darderi or Dutchman Tallon Griekspoor.
