Medvedev will tackle third seed and previous rival Stefanos Tsitsipas within the semi-finals.
The Greek survived a scare against big-serving John Isner on Friday.
Depending on his serve to take the primary set into the tiebreak, Tsitsipas was given little luck as rain interrupted the breaker, after which he got out to take the stage.
Isner took a late break on the finish of the second and took the match into the decider, however Tsitsipas confirmed his capability to soak up the strain by profiting from his one and solely break level within the third and gained the match 7-6(5) . ), 5-7, 6-3.
Medvedev and Tsitsipas will meet for the tenth time on tour with an typically private, rivalry since they famously bought collectively in Miami in 2018. Medvedev goes face to face 7-2, however the Greek has gained 2 of his final 4.