Chile's Tabilo will play his first-ever last four match at a Masters 1000 event at the age of 26, after unfussily seeing off unseeded Zhang 6-3, 6-4 in one hour and 26 minutes on centre court at the Foro Italico.
Tabilo knocked out six-time Rome champion Novak Djokovic on Sunday and in the last four will face Alexander Zverev after the German defeated Taylor Fritz 6-4, 6-3.
"It's just unbelievable, I just can't believe it right now, still trying to soak this in... Definitely an unforgettable two weeks for me," said a delighted Tabilo.
"It's definitely the best tennis of my life right now, but I mean, trying to keep a poker face there because inside I'm just so nervous, every time trying to close out the match gets a little bit tighter."
Tabilo, in fact, had far less trouble on Wednesday than he did in his battle with Karen Khachanov in the previous round, not facing a single break point on his way to the biggest match of his career at the last major tournament before the French Open.
Zverev reached his 18th Masters semi-final but only after a worrying fall which sparked memories of the horror injury he suffered at the French Open two years ago
Zverev's moment of concern came in just the third game on centre court at the Foro Italico when he fell on the clay and landed on his front.
The 2017 champion cut his left wrist and a finger in the tumble and required treatment from the tournament physio before he continued the match.
Zverev suffered a serious ankle injury at the 2022 French Open after falling on the clay of Roland Garros during his semi-final against Rafael Nadal and missed the rest of the season.
On Wednesday, however, he was able to dust himself down to defeat Fritz in 90 minutes, firing 20 winners with six aces and not facing a single break point.
Zverev is the highest-ranked man left in the event after Daniil Medvedev's elimination on Tuesday.
As well as Djokovic's exit, Italian world number two Jannik Sinner and third-ranked Carlos Alcaraz both dropped out injured before the tournament.
Holger Rune, who lost last year's final to Medvedev, Madrid champion Andrey Rublev - ranked sixth in the world - and beaten finalist Felix Auger-Aliassime have also been eliminated.
