Fifth seed Ruud showed he could go the distance having survived an extraordinary 55-shot rally to close the first-set tie-break and next faces either home hope Frances Tiafoe (24) or third seed Carlos Alcaraz (19) of Spain in the final.
The Roland-Garros runner-up is known for his poise on clay but proved equally effective on New York's hard courts, winning 14 straight points to build a 5-1 lead in a near-flawless second set.
His form deteriorated in the third set, where he racked up 11 unforced errors and handed Khachanov the break on set point, but he bounced back to convert breaks on chances in the third and fifth game of the fourth set and clinched the contest with a forehand winner, one of 20 across the match.
This match is probably the biggest match for both of our careers," said Ruud, who was left humbled when he lost in straight sets to Rafa Nadal in June's Roland Garros final.
"You want to take care of the opportunities you have and I was able to do that today."
Check out all the statistics from the first men's semi-final with Flashscore.
