Zverev overcame Bellucci on the grass courts in Nottingham last month and the 18-year-old was too good again for the world number 41, coming from behind to win 5-7 6-4 6-2.
The match lasted two hours and 28 minutes and Zverev’s victory means he will now play Spanish veteran Tommy Robredo in the last four.
“He played unbelievable the first two sets,” Zverev told atpworldtour.com.
“So I just had to get into the match somehow and luckily I got the win in the end.
“I’m really happy to be in the semi-finals. I’m looking forward to tomorrow.”
Robredo’s passage was more straightforward as he eased past qualifier Paul-Henri Mathieu 6-3 6-3.
The 33-year-old Spaniard has already been crowned champion twice in Bastad, having won the tournament in 2006 and 2008.
Uruguay’s Pablo Cuevas took a step closer to defending his title after he knocked out Belgian Steve Darcis 6-3 6-4.
Cuevas, whose triumph in Bastad last year was his first ATP success, will now play France’s Benoit Paire, who beat Denis Istomin 6-4 6-2.