Fritz will play the semi-final against the winner of unseeded Briton Cameron Norrie and two-time Wimbledon champion Carlos Alcaraz.
The Californian has always been proficient on grass, where he has won his last three titles, including Eastbourne just last month on the British coast. He now finds himself in fine form with a 13-1 record on the surface this season going into the semis at SW19.
With Fritz dominating the opening two sets in 76 minutes, the Paris 2024 doubles bronze medallist stood a set away from the final four.
But Khachanov refused to back down so easily, roaring back in style by winning eight out of the next nine games from the third set onwards. The Olympic silver medallist was rejuvenated, pushing the fifth seed to brink after the third set.
27-year-old Fritz recovered from 0-2 down in the fourth to work his way back into the lead, though could not prevent a fourth set tiebreak with his opponent fighting for a fifth. He conceded his 4-1 tiebreak lead as Khachanov roared his way back into it, but when the moment arose, Fritz was clinical with a double mini break to prevail.