"Obviously that's not how I wanted the game to end," said the 26-year-old Russian, saying "it was a tight game up to a point".
"He had beaten my buddy Daniil (Medvedev) in three sets and Hubert (Hurkacz) in five sets, so we know he's playing well," Khachanov added of Korda.
Already semi-finalist of the last US Open, Khachanov will face the Greek Stefanos Tsitsipas (4th) or the Czech Jiri Lehecka (71st) on Friday for a place in the final.
He had never made it past the third round in Melbourne.
He immediately took the lead in the first set on Tuesday by breaking away 3-0.
But Korda took advantage of a drop in efficiency from the Russian on his serve as he served at 5-3 to win the set, to catch up and take Khachanov to the tiebreaker.
The latter had three set points and concluded on the third.
From the start of the second set, Korda was under threat from Khachanov: he had to save a break point in the first game, then two in the third.
At the end of the fifth, when he was leading 3-2, the American had his right wrist treated on the court.
From there, the game changed: Khachanov won the next seven games before Korda threw in the towel.
© 2023 AFP