Beaten US Open finalist Medvedev showed little sign of a hangover from his exertions in New York in his Round of 16 tie against fellow Russian Evgeny Donskoy on Thursday (AEST), and the 23-year-old continued his fine form against a player who claimed some big scalps in the North American hard-court swing.
Rublev, who overcame Stefanos Tsitsipas and Nick Kyrgios at Flushing Meadows, beat Roger Federer on his way to meeting Medvedev at the Western & Southern Open in August, an encounter the latter won 6-2 6-3 en route to a maiden ATP 1000 title.
The world No.4 came out on top again this time around, although it was tighter affair as Medvedev prevailed 6-4 7-5, breaking serve three times in succession in the second set.
Medvedev will face Egor Gerasimov in the last four, with the qualifier having upset the odds to stun No.3 seed Matteo Berrettini 7-6 (7-5) 7-6 (7-3).
No.4 seed Borna Coric will go head-to-head with Joao Sousa in the other semi-final.
Meanwhile, Nikoloz Basilashvili retired hurt to hand Jo-Wilfried Tsonga passage into the Moselle Open semi-finals.
No.2 seed Basilashvili came through a gruelling first set 7-5 in Metz, but Frenchman Tsonga, who is now No.61 in the singles rankings, rallied to restore parity before taking a 4-1 lead in the final set prior to his opponent's retirement.
Tsonga will face Lucas Pouille after his victory over Filip Krajinovic, while No.3 seed Benoit Paire goes up against Aljaz Bedene.