No.1 seed Alcaraz needed an hour and nine minutes to beat Russian Khachanov 6-0 6-2 in a clay-court masterclass on Saturday (AEST).
The 19-year-old Spaniard moved a step closer to winning a fifth title this year with a dominant performance, breaking the Russian five times in a one-sided contest.
Alcaraz hit 21 winners as Khachanov was given a harsh lesson and the teenager will next face Alex Molcan, who was 2-0 up in the second set after winning the first on a tie-break when Borna Coric retired because of injury.
"I played unbelievable today, probably one of my best matches this year," Alcaraz said of his win against Khachanov. "I'm pretty happy with the performance that I'm playing in this tournament. Yesterday [a victory over Filip Krajinovic] was amazing as well.
"I'm training every day to be solid and at the same time to be aggressive. That is my game."
Francisco Cerundolo and Lorenzo Musetti will contest the other semi-final in Hamburg after beating Aslan Karatsev and Alejandro Davidovich Fokina respectively.
A rejuvenated Thiem is enjoying another hugely encouraging week and will take on Berrettini in his first semi-final of the year after a 6-4 6-3 defeat of Peruvian qualifier Juan Pablo Varillas in Gstaad.
Austrian Thiem has not played in a final since winning his only grand slam at the 2020 US Open, but he claimed his first ATP-level victory for 14 months in Bastad last week and is through to his first semi-final since May 2021 after bossing the baseline battle with Varillas.
It was not all plain sailing for Berrettini, who roared back to beat Pedro Martinez 3-6 7-6 (7-5) 6-1 after the Spaniard was in command of a second-set tie-break at 5-1, but the second seed extended his winning run to 11 matches.
No.1 seed Casper Ruud got the better of Jaume Munar 7-6 (7-3) 7-6 (7-4), booking a showdown with Albert Ramos-Vinolas, who came through a three-set battle with Nicolas Jarry.