The Austrian fourth seed struggled early in the tournament but has warmed to the task and was far too solid for the 23-year-old Khachanov, who was unable to replicate the tennis he produced to beat Juan Martin del Potro in the previous round.
Thiem, runner-up to Rafael Nadal last year, hardly put a foot wrong throughout a one-sided conest as he set up a clash with either top seed Novak Djokovic.
Khachanov had won their only previous meeting, also in Paris but on an indoor hardcourt. However, Thiem on clay is an entirely different proposition and from the moment Khachanov struggled to hold serve in the opening game his prospects looked bleak.
The razor-sharp Thiem broke serve in the third game and never relinquished control, offering Khachanov not even a sniff of a break point throughout a clinical display.