Khachanov, at 22 another of the sport's brightest prospects, took ruthless advantage of the 21-year-old German's physical struggles as Zverev, battling with shoulder trouble, needed a medical time out in the first set at 4-1 down.
The Muscovite deserved all the credit for the quality of his power game, however, as he broke the world number five's serve six times in 70 minutes to set up a date with Austrian Thiem, who later beat champion Jack Sock 4-6 6-4 6-4.
Zverev looked frustrated at his serving woes and being pushed around by the world number 18. At the end of a one-sided first set, he complained to Khachanov about the over-zealous reactions of the Russian's camp at courtside.
"When you are losing, maybe you get frustrated from some calls from somebody in the crowd," Khachanov told Sky Sports.
"But then we're good friends outside the court and everything is fine."
Zverev, who has qualified for the ATP Tour Finals for the second year running, offered his point of view.
"I told him my shoulder is hurting and that his uncle, or something, that he's going a bit crazy," he said.
"I was never going to win the match, so it was just I told him to calm down a little bit."
Zverev had defeated Khachanov in their previous two meetings, including a five-setter at the French Open in June, but the Russian dominated from the outset this time.
"It was really tough for me to lose that match in Paris," said Khachanov, who had been leading two sets to one at Roland Garros.
"So I was fully prepared, I've been playing some good tennis in the last couple of months and believing in myself so I didn't expect to be that easy in the score."
With two indoor hardcourt tournament triumphs to his name this year, Khachanov will move up to at least a career-high number 13 in the world next week.
Sock had made an unexpected return to form after a wretched year since his surprise Paris triumph but his renaissance was ended when Thiem fought from a set down to take control in a tough two-and-a-quarter hour duel.
The victory gave French Open finalist Thiem a further boost in his bid to earn one of the final two of eight places on offer for the ATP Finals in London this month.
"Jack was playing a great game and had a very good start and it was a great fight again, but it's really something special for me to reach this stage," world number eight Thiem said.
In the evening session in Bercy, Novak Djokovic, fresh from regaining his world number one ranking, plays Marin Cilic and could set up the other semi-final against Roger Federer, who faces Japan's Kei Nishikori. (Reporting by Ian Chadband; editing by Martyn Herman and Ed Osmond)
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