Alcaraz, 19, is defending the first ATP title he won in the coastal town of Umag last year.
Fifth-ranked Alcaraz, from Spain, saved the only break point he faced as he improved his 2022 record on clay to 26-3.
Zeppieri failed to serve the match out at 6-5 in the second set before prevailing in the tiebreaker.
“I’m very happy, obviously,” Sinner said. “I’ve won many matches but I think I’ve had some unfortunate moments this year.”