World No.287 Ebden upset 2018 champion Khachanov from Russia, 4-6 6-4 6-2, putting him in the firing line of Khachanov countryman Medvedev in Sunday's (AEDT) semi-final.
No.1 seed Medvedev, who will replace Rafael Nadal as world No.2 on Monday, eased to a 6-2 6-4 victory against 19-year-old Italian Jannik Sinner in his match.
Medvedev, who has nine career titles, is through to his first semi-final in Marseille, after falling in the quarter-finals in 2017 and 2020.
"Jannik always tries to hit the ball as hard as he can," Medvedev said.
"You cannot give him easy balls, otherwise you are going to run all over the place and he is probably going to hit a winner."
Greek world No.5 Stefanos Tsitsipas also saw his hopes of a third successive Marseille ATP title dashed by No.93-ranked Pierre-Hugues Herbert in another quarter-final shock.
Herbert, better known as a doubles specialist, swept past Australian Open semi-finalist Tsitsipas 6-7 (6-8) 6-4 6-2.
The 29-year-old will next face a fellow Frenchman, Ugo Humbert or Arthur Rinderknech, for a place in the final.
"It's incredible, it's my first win against a top-five player," Herbert said.
"I knew that I'd have to play a great match to win and that's what I did."