Zverev battles into Halle semis, joined by Medvedev
The German second seed felled Cobolli 6-4, 7-6 (8/6) and will next face Daniil Medvedev, after the Russian third seed beat American Alex Michelsen 6-4, 6-3 in his quarter-final.
In a rematch of a third-round meeting at Roland Garros three weeks ago, Zverev again produced an impressive serving performance.
He crucially rallied from 0-40 down in the second and fourth games of first set.
A finalist in Stuttgart last week Zvervev will be hoping to go one better on the grass of Halle after being a losing finalist at the tournament in 2016 and 2017.
It wasn't all plain sailing as he had to take an unscheduled break at 1-1 and deuce in the first set.
"I felt fine before the match, and then out of nowhere I felt really, really bad and felt ill," recounted Zverev.
"I went to throw up, and then 15 minutes later I felt okay again. So I don't know what it was. I've never experienced that before, to be honest. Hopefully I will be fine the next couple of hours, when the adrenalin settles. After that, I think it was a pretty good match."
He sealed the contest with a big first serve in the second set tie-break.
Medvedev earlier reached his third semi of the season.
He is guaranteed to return to the Top 10 in the ATP rankings.
Zverev, who last met Medvedev in the 2024 Australian Open semi-finals, said: "Definitely he's one of the toughest opponents in my career. It's going to be a great match and I'm really looking forward to facing him."
In the other quarter-finals, Alexander Bublik, who claimed defending champion and world number one Jannik Sinner's scalp on Wednesday, plays Tomas Machac with Tomas Martin Etcheverry up against Karen Khachanov.