The Greek, who a day earlier secured his place as one of the eight qualifiers for the ATP Finals in Turin, was at his shot-making best to dominate the contest.
He will now face Grigor Dimitrov (32) for a place in the final after the Bulgarian beat Hubert Hurkacz (26) 6-1, 4-6, 6-4.
Seventh seed Tsitsipas is yet to drop a set this week in disposing of Canada's Felix Auger-Aliassime (23), Germany's Alexander Zverev (26) and now Khachanov.
He had far too much variety for Khachanov in the opening set, using his all-court game and accurate serving to great effect. He then moved a break ahead in the second set before Khachanov hit a brief purple patch to get back on terms.
But Tsitsipas quickly regained control to sweep to the 300th professional win of his career, bringing up match point with a delightful drop shot that had the crowd in raptures.
"It's working well. It feels good to have so much variety and so much diversity in the way you can play," he said.
"I take that as an opportunity to keep growing my game and keep looking forward at the many more matches to come and appreciate each moment that comes my way."
Hurkacz's defeat by Dimitrov ended his hopes of qualifying for the ATP Finals.
Djokovic downs Rune
Later on Friday, world number one Novak Djokovic (36) stayed on course for a seventh Paris Masters title with a gripping 7-5, 6-7, 6-4 defeat of Holger Rune (20) in the quarter-finals on Friday which left the Dane sweating on a place in the ATP Tour Finals.
Djokovic was rock solid as he avenged his defeat by the tenacious youngster in last year's showpiece to set up a semi-final against either Andrey Rublev or Alex de Minaur.
Victory for Rune would have sealed his place in Turin although he is still well-placed to make his debut in the year-ender featuring the world's top eight players.
Djokovic's victory means Germany's Alexander Zverev (26) qualifies for the ATP Tour Finals.
Rune delighted the Paris crowd with some stunning tennis and saved a match point at 4-5 in the second set before an inspired tiebreak took the match to a decider.
But Djokovic was unfazed and broke serve early in the third set, while Rune was not helped by a cut to his hand that required some lengthy patching up at a changeover.
The sixth seed could make no impression on the Djokovic serve in the decider as the top-ranked Serb clocked up a 16th successive win since losing in the Wimbledon final.
